Percentage problems (applied practice)

{"questions":[{"content":"In the sports section, girls make up $70\\%$ of the total number of participants. How many participants are there in the section if there are $60$ more girls than boys?[[fill_choice_big-2]][[image-3715]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$140$","$150$","$160$"],"placeholder":0,"answer":1},"image-3715":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/sport-01.svg","width":"300"}},"hints":["Let us denote the total number of participants in the section as $x.$ <br />Girls make up $70\\%$ from all participants.<br />Boys make up the remaining $30\\%.$<br />According to the condition, there are more girls in $60$ than boys. <br /><br />Write the equation: $$0.7x=0.3x+60$$ Solve the equation: $$0.7x-0.3x=60$$$$0.4x=60$$$$x=\\frac{60}{0.4}=150$$ The total number of participants in the section is $150$."]},{"content":"The number of road traffic accidents (RTA) in the summer was $0.85$ the number of accidents in the winter. By what percentage did the number of traffic accidents decrease in summer compared to winter?[[fill_choice_big-28]][[image-3738]]","widgets":{"fill_choice_big-28":{"type":"fill_choice_big","options":["$15$","$14$","$13$"],"placeholder":0,"answer":0},"image-3738":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/04/policziya-policzeskij-uchastok-mashina-zdanie-dom-2.svg","width":"300"}},"hints":["Take the number of road accidents in winter as $100\\%.$<br /><br />Then the number of road accidents in the summer will be - $85\\%.$ <br /><br />Find the difference: $$100\\%-85\\% = 15\\%$$The number of accidents decreased by $15\\%.$<br /><br />"]},{"content":"In a sports store, any sweater costs $500$ rubles. Now the store is running a promotion: if you buy two sweaters, you get a discount on the second sweater $60\\%.$ How many rubles will you have to pay for buying two sweaters during the promotion period? [[fill_choice_big-43]][[image-3763]]","widgets":{"fill_choice_big-43":{"type":"fill_choice_big","options":["$700$","$750$","$780$"],"placeholder":0,"answer":0},"image-3763":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2025/02/obrazavr_shkaf-s-odezhdoj-01-1.svg","width":"300"}},"hints":["The price of the first sweater is $500$ rubles.<br />Price of the second sweater at a discount $60\\%{:}$ $$500-0.60\\cdot500=200\\space rubles$$ Total cost of two sweaters: $$500+200=700\\space rubles$$ For the purchase of two sweaters you will have to pay - $700$ rubles.<br /><br />"]},{"content":"In a bookstore, any book costs $400$ rubles. The store is currently running a promotion: when purchasing two books, the discount on the second book is $50\\%.$ How many rubles will you have to pay for purchasing two books during the promotion period? [[fill_choice_big-97]][[image-3790]]","widgets":{"fill_choice_big-97":{"type":"fill_choice_big","options":["$600$","$650$","$700$"],"placeholder":0,"answer":0},"image-3790":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/kniga_nauka-chitaet-obrazavr-01-01.svg","width":"300"}},"hints":["The price of the first book is $400$ rubles.<br />Price of the second book at a discount $50\\%{:}$ $$400-0.50\\cdot400=200\\space rubles$$ Total cost of two books: $$400+200=600\\space rubles$$ You will have to pay for the purchase of two books - $600$ rubles.<br /><br />"]},{"content":"A quarter of all vacationers in the boarding house are children. What percentage of all vacationers are children?[[fill_choice_big-174]][[image-3819]]","widgets":{"fill_choice_big-174":{"type":"fill_choice_big","options":["$25$","$50$","$40$"],"placeholder":0,"answer":0},"image-3819":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/09/v-pesochnicze.svg","width":"300"}},"hints":["Children make up $\\dfrac{1}{4}$ of all vacationers in the boarding house.<br /><br />To convert the fraction into a percentage, multiply by $100{:}$ $$\\frac{1}{4}\\cdot100\\%=25\\%$$Children make up $25\\%$ of all vacationers."]},{"content":"In the class $25$ students. Of these, $20\\%$ received A marks for the test. How many students got A's? [[fill_choice_big-257]][[image-3850]]","widgets":{"fill_choice_big-257":{"type":"fill_choice_big","options":["$5$","$7$","$6$"],"placeholder":0,"answer":0},"image-3850":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/05/obrazavr_deyatelnost_dop-04-2.svg","width":"300"}},"hints":["To find $20\\%$ from $25,$ let's perform the calculation: $$0.20\\cdot25=5$$ $5$ students received A's."]},{"content":"There were $80\\space kg$ apples in the store. In one day we sold $30\\%$ of all apples. How many kilograms of apples are left in the store?[[fill_choice_big-410]][[image-3883]]","widgets":{"fill_choice_big-410":{"type":"fill_choice_big","options":["$56$","$51$","$57$"],"placeholder":0,"answer":0},"image-3883":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/09/yabloko-solntse-yablonya.svg","width":"300"}},"hints":["Find how many kilograms of apples were sold: $$0.30\\cdot80=24$$ Now find how many kilograms of apples are left: $$80-24=56$$ There are: $56\\space kg$ apples left in the store.<br /><br />"]},{"content":"There are $800$ students at school. Of these, $25\\%$ are in primary school, $35\\%$ are in middle school, and the rest are in high school. How many students are in high school?[[fill_choice_big-22]][[image-3918]]","widgets":{"fill_choice_big-22":{"type":"fill_choice_big","options":["$320$","$380$","$360$"],"placeholder":0,"answer":0},"image-3918":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/shkolniki-klass-party-parta-okno-stulya-stoly-sidyat-za-partoi-.svg","width":"300"}},"hints":["Find the number of students in primary school: $$0.25\\cdot800=200$$ Find the number of students in middle school: $$0.35\\cdot800=280$$ Find the number of students in high school: $$800-200-280=320$$ There are $320$ students in high school."]},{"content":"At the university $1\\space500$ students. Of these, $30\\%$ study in technical specialties, $40\\%$ in humanities, and the rest in natural sciences. How many students are enrolled in science majors? [[fill_choice_big-321]][[image-3955]]","widgets":{"fill_choice_big-321":{"type":"fill_choice_big","options":["$450$","$480$","$430$"],"placeholder":0,"answer":0},"image-3955":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/11/obrazavr_break.svg","width":"299"}},"hints":["Find the number of students in technical specialties: $$0.30\\cdot1\\space500=450$$ Find the number of students in humanities specialties: $$0.40\\cdot1\\space500=600$$ Find the number of students in natural science specialties: $$1\\space500-450-600=450$$ $450$ students study in natural science specialties."]},{"content":"The football team has $20$ players. $25\\%$ of them are forwards, $35\\%$ are midfielders, and the rest are defenders and goalkeepers. How many players on the team are defenders and goalkeepers?[[fill_choice_big-404]][[image-3994]]","widgets":{"fill_choice_big-404":{"type":"fill_choice_big","options":["$9$","$8$","$10$"],"placeholder":0,"answer":1},"image-3994":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/futbolisty-01-01.svg","width":"300"}},"hints":["Find the number of forwards: $$0.25\\cdot20=5$$ Find the number of midfielders: $$0.35\\cdot20=7$$ Find the number of defenders and goalkeepers: $$20-5-7=8$$ Defenders and goalkeepers in the team - $8$."]}]}

{"questions":[{"content":"The client took out a loan from the bank $12\\space000$ rubles for a year under $16\\%.$. He must repay the loan by depositing the same amount of money into the bank every month, in order to pay off the entire amount borrowed along with interest in a year. How many rubles should he deposit into the bank monthly?[[fill_choice_big-46]][[image-2785]]","widgets":{"fill_choice_big-46":{"type":"fill_choice_big","options":["$1\\space160$","$1\\space180$","$1\\space170$"],"placeholder":0,"answer":0},"image-2785":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/dengi.svg","width":"300"}},"hints":["Find the amount of interest for the year: $$0.16\\cdot12\\space000=1\\space920\\space rubles$$ Determine the total amount to be returned: $$12\\space000+1\\space920=13\\space920\\space rubles$$ Divide the total amount by $12$ months to find the monthly payment: $$\\frac{13\\space920}{12}=1\\space160\\space rubles$$ The client must pay $1\\space160$ rubles to the bank monthly."]},{"content":"Income tax is $13\\%$ from wages. After withholding income tax, Maria Konstantinovna received $9\\space570$ rubles. How many rubles is Maria Konstantinovna’s salary?[[fill_choice_big-22]][[image-2808]]","widgets":{"fill_choice_big-22":{"type":"fill_choice_big","options":["$11\\space000$","$11\\space300$","$11\\space700$"],"placeholder":0,"answer":0},"image-2808":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/11/svobodnoe13.svg","width":"303"}},"hints":["After withholding income tax, Maria Konstantinovna received $9\\space570$ rubles. This amounts to $87\\%$ of wages.<br />Convert the percentages into decimal fractions and calculate the value: $$\\frac{9\\space570}{0.87}=11\\space000$$ Maria Konstantinovna's salary is $11\\space000$ rubles."]},{"content":"Income tax is $13\\%$ from wages. After withholding income tax, Polina Olegovna received $44\\space631$ ruble. How many rubles is Polina Olegovna’s salary?[[fill_choice_big-7]][[image-2833]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$51\\space300$","$51\\space400$","$51\\space600$"],"placeholder":0,"answer":0},"image-2833":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/bankomat-01.svg","width":"300"}},"hints":["After withholding income tax, Polina Olegovna received $44\\space631$ ruble. This amounts to $87\\%$ of wages.<br />Convert the percentages into decimal fractions and calculate the value: $$\\frac{44\\space631}{0.87}=51\\space300$$ Polina Olegovna's salary is $51\\space300$ rubles."]},{"content":"The school has $800$ students, of which $30\\%$ are elementary school students. Middle and high school students at $20\\%$ are studying German. How many students study German in school if German is not taught in primary school?[[fill_choice_big-1]][[image-2860]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$112$","$110$","$118$"],"placeholder":0,"answer":0},"image-2860":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/sidyat-za-partoj-ruchka.svg","width":"300"}},"hints":["Find the number of elementary school students: $$0.3\\cdot800=240$$ Determine the number of middle and high school students: $$800-240=560$$ Find the number of students studying German: $$0.2\\cdot560=112$$ $112$ students study German."]},{"content":"Among $40\\space000$ city residents, $60\\%$ is not interested in football. Among the football fans, $80\\%$ watched the Champions League final on TV. How many city residents watched this match on TV?[[fill_choice_big-120]][[image-2889]]","widgets":{"fill_choice_big-120":{"type":"fill_choice_big","options":["$12\\space600$","$12\\space800$","$12\\space900$"],"placeholder":0,"answer":1},"image-2889":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/gorod-lyudi-zanyatoj-mashiny-1-1.svg","width":"300"}},"hints":["Find the number of residents who are not interested in football: $$0.6\\cdot40\\space000=24\\space000$$ Determine the number of football fans: $$40\\space000-24\\space000=16\\space000$$ Find the number of fans who watched the Champions League final: $$0.8\\cdot16\\space000=12\\space800$$ The Champions League final was watched by $12\\space800$ residents of the city."]},{"content":"Among $50\\space000$ residents of the city $70\\%$ are not interested in hockey. Among the hockey fans, $60\\%$ watched the Stanley Cup final on TV. How many city residents watched this match on TV?[[fill_choice_big-26]][[image-2920]]","widgets":{"fill_choice_big-26":{"type":"fill_choice_big","options":["$9\\space000$","$9\\space200$","$9\\space300$"],"placeholder":0,"answer":0},"image-2920":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/konki-katok-les-elka-zima-kataetsya.svg","width":"302"}},"hints":["Find the number of residents who are not interested in hockey: $$0.7\\cdot50\\space000=35\\space000$$ Determine the number of hockey fans: $$50\\space000-35\\space000=15\\space000$$ Find the number of fans who watched the Stanley Cup final: $$0.6\\cdot15\\space000=9\\space000$$ The Stanley Cup final was watched by $9\\space000$ residents of the city."]},{"content":"The student received his first fee in the amount of $700$ rubles for the completed translation. He decided to use all the money he received to buy a bouquet of tulips for his English teacher. What is the largest number of tulips a student can buy if the income tax withheld from him is $13\\%$ fee, and tulips cost $60$ rubles per piece and the bouquet must consist of an odd number of flowers? [[fill_choice_big-125]][[image-2953]]","widgets":{"fill_choice_big-125":{"type":"fill_choice_big","options":["$9$","$10$","$11$"],"placeholder":0,"answer":0},"image-2953":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/student-01-1.svg","width":"300"}},"hints":["Find the amount of income tax: $$0.13\\cdot700=91\\space ruble$$ Determine the amount that the student will receive after withholding tax: $$700-91=609\\space rubles$$ Find how many tulips can be bought for $609$ rubles: $$\\frac{609}{60}=10.15$$ There is enough money for $10$ tulips. The bouquet must have an odd number of flowers, so the student will buy $9$ tulips."]},{"content":"The student received his first fee in the amount of $1\\space600$ rubles. He decided to use all the money he received to buy a bouquet of tulips for his girlfriend. What is the largest number of tulips a student can buy if the income tax withheld from him is $6\\%$ fee, and tulips cost $90$ rubles per piece and the bouquet must consist of an odd number of flowers? [[fill_choice_big-92]][[image-2988]]","widgets":{"fill_choice_big-92":{"type":"fill_choice_big","options":["$15$","$16$","$17$"],"placeholder":0,"answer":0},"image-2988":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/02/czvetok-gorshok-czvetochnyj.svg","width":"300"}},"hints":["Find the amount of income tax: $$0.06\\cdot1\\space600=96\\space rubles$$ Determine the amount that the student will receive after withholding tax: $$1\\space600-96=1\\space504\\space rubles$$ Find how many tulips can be bought for $1\\space504$ ruble: $$\\frac{1\\space504}{90}\\approx16.71$$ There is enough money for $16$ tulips. The bouquet must have an odd number of flowers, so the student will buy $15$ tulips."]},{"content":"The number of coniferous trees in the park is related to the number of deciduous trees as $9:16.$ There are no other trees in the park. What percentage of the trees in the park are deciduous?[[fill_choice_big-159]][[image-3025]]","widgets":{"fill_choice_big-159":{"type":"fill_choice_big","options":["$64$","$66$","$65$"],"placeholder":0,"answer":0},"image-3025":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/01/park-1.svg","width":"301"}},"hints":["Find the total number of trees in the park: $$9+16=25$$ Calculate the percentage of deciduous trees: $$\\frac{16}{25}\\cdot100\\%=64\\%$$ Thus, deciduous trees make up $64\\%.$"]},{"content":"At school, girls make up $60\\%$ the number of all students. How many students are there in this school if there are $105$ more girls than boys?[[fill_choice_big-390]][[image-3064]]","widgets":{"fill_choice_big-390":{"type":"fill_choice_big","options":["$525$","$565$","$515$"],"placeholder":0,"answer":0},"image-3064":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/mnozhestvo.svg","width":"300"}},"hints":["Let us denote the total number of students in the school as $x.$<br />There are more girls than boys by $20\\%$ of the total number of students. This can be written as:$$0.6x-0.4x=0.2x$$According to the conditions of the problem, there are $105$ more girls than boys.$$0.2x=105$$Solve the equation:$$x=\\frac{105}{0.2}=525$$The total number of students in the school is $525.$"]}]}

{"questions":[{"content":"The store buys books at a wholesale price of $460$ rubles per piece and sells them at a premium $60\\%.$ How many rubles will two such books bought in this store cost? [[fill_choice_big-1]][[image-1873]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$1\\space427$","$1\\space472$","$1\\space416$"],"placeholder":0,"answer":1},"image-1873":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/kniga_nauka-chitaet-obrazavr-01-01.svg","width":"300"}},"hints":["Find the markup on one book: $$0.6\\cdot460=276\\space rubles$$ Determine the retail price of one book: $$460+276=736\\space rubles$$ Find the cost of two books: $$2\\cdot736=1\\space472\\space rubles$$ Two books will cost $1\\space472$ rubles."]},{"content":"At school, $153$ students study French, which is $30\\%$ of all school students. How many students are there in the school?[[fill_choice_big-16]][[image-1918]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$510$","$490$","$470$"],"placeholder":0,"answer":0},"image-1918":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/02/francziya-franczuz-3.svg","width":"300"}},"hints":["Convert the percentages to a decimal fraction and calculate the value: $$\\frac{153}{0.3}=510$$At school there are $510$ students."]},{"content":"In the class, $7$ students study German, which is $25\\%$ of all students in the class. How many students are in the class?[[fill_choice_big-94]][[image-1943]]","widgets":{"fill_choice_big-94":{"type":"fill_choice_big","options":["$28$","$30$","$32$"],"placeholder":0,"answer":0},"image-1943":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/germaniya-flag-doma-zdaniya-dom.svg","width":"300"}},"hints":["Convert the percentages to a decimal fraction and calculate the value: $$\\frac{7}{0.25}=28$$In the class $28$ students."]},{"content":"Income tax is $13\\%$ from wages. Ivan Kuzmich's salary is $11\\space000$ rubles. What amount will he receive after deducting income tax?[[fill_choice_big-115]][[image-1970]]","widgets":{"fill_choice_big-115":{"type":"fill_choice_big","options":["$9\\space590$","$9\\space570$","$9\\space560$"],"placeholder":0,"answer":1},"image-1970":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/koshelek-2.svg","width":"300"}},"hints":["Find the amount of income tax: $$0.13\\cdot11\\space000=1\\space430\\space rubles$$ Determine the amount that Ivan Kuzmich will receive after deducting the tax: $$11\\space000-1\\space430=9\\space570\\space rubles$$ After deducting the income tax, Ivan Kuzmich will receive $9\\space570$ rubles."]},{"content":"At the beginning of the school year there were $500$ students in the school, and by the end of the year<br />their number became $600.$ By what percentage did the number of students increase during the school year?[[fill_choice_big-146]][[image-1999]]","widgets":{"fill_choice_big-146":{"type":"fill_choice_big","options":["$20$","$15$","$30$"],"placeholder":0,"answer":0},"image-1999":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/shkolniki-klass-party-parta-okno-stulya-stoly-sidyat-za-partoi-.svg","width":"300"}},"hints":["Determine by how many people the number of students has increased: $$600-500=100$$ Find what percentage this increase is from the initial number of students: $$\\frac{100}{500}\\cdot100\\%=20\\%$$ The number of students has increased by $20\\%.$"]},{"content":"Ballpoint pen costs $40$ rubles. What is the largest number of such pens that can be bought for $900$ rubles after the price increases by $10\\%?$[[fill_choice_big-260]][[image-2030]]","widgets":{"fill_choice_big-260":{"type":"fill_choice_big","options":["$20$","$30$","$25$"],"placeholder":0,"answer":0},"image-2030":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/ruchka.svg","width":"300"}},"hints":["Find the new price of a pen after an increase of $10\\%{:}$ $$0.1\\cdot40=4$$$$40+4=44\\space rubles$$Determine how many pens can be bought for $900$ rubles:$$\\frac{900}{44}\\approx20.45$$Since you cannot buy part of a pen, round down to the nearest integer. <br /><br />The largest number of pens you can buy is $20$."]},{"content":"The notebook costs $30$ rubles. What is the largest number of such notebooks that can be purchased for $500$ rubles after the price has been lowered by $15\\%?$[[fill_choice_big-350]][[image-2063]]","widgets":{"fill_choice_big-350":{"type":"fill_choice_big","options":["$20$","$19$","$21$"],"placeholder":0,"answer":1},"image-2063":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/tetradki-1.svg","width":"300"}},"hints":["Find the new price of a notebook after lowering it by $15\\%{:}$ $$0.15\\cdot30=4.5$$$$30-4.5=25.5\\space rubles$$ Determine how many notebooks can be bought for $500$ rubles: $$\\frac{500}{25.5}\\approx19.61$$ Since you can't buy part of a notebook, we round down to the nearest whole number.<br /><br />The largest number of notebooks that can be purchased is $19.$"]},{"content":"Wholesale price of the textbook $170$ rubles. The retail price for $20\\%$ is higher than the wholesale price. What is the largest number of such textbooks that can be purchased at a retail price of $7\\space000$ rubles?[[fill_choice_big-197]][[image-2098]]","widgets":{"fill_choice_big-197":{"type":"fill_choice_big","options":["$34$","$36$","$38$"],"placeholder":0,"answer":0},"image-2098":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/sitting-on-books-v2.svg","width":"300"}},"hints":["Find the retail price of a textbook: $$0.2\\cdot170=34$$$$170+34=204\\space rubles$$ Determine how many textbooks can be bought for $7\\space000$ rubles: $$\\frac{7\\space000}{204}\\approx34.31$$ Since you can't buy part of a textbook, we round down to the nearest whole number.<br /><br />The largest number of textbooks that can be purchased is $34.$"]},{"content":"A train ticket for an adult costs $720$ rubles. The cost of a ticket for a schoolchild is $50\\%$ of the cost of a ticket for an adult. The group consists of $15$ schoolchildren and $2$ adults. How many rubles are tickets for the whole group?[[fill_choice_big-282]][[image-2135]]","widgets":{"fill_choice_big-282":{"type":"fill_choice_big","options":["$6\\space840$","$6\\space480$","$6\\space640$"],"placeholder":0,"answer":0},"image-2135":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/poezd-stancziya-.svg","width":"300"}},"hints":["Find the cost of a ticket for a schoolchild: $$0.5\\cdot720=360\\space rubles$$ Calculate the cost of tickets for $15$ schoolchildren: $$15\\cdot360=5\\space400\\space rubles$$ Calculate the cost of tickets for $2$ adults: $$2\\cdot720=1\\space440\\space rubles$$ Find the total cost of tickets for the whole group: $$5\\space400+1\\space440=6\\space840\\space rubles$$ Tickets for the whole group cost $6\\space840$ rubles."]},{"content":"$200\\space000$ residents live in the city of $N$. Among them are $15\\%$ children and teenagers. $45\\%$ does not work among adult residents (pensioners, students, housewives, etc.). How many adult residents work?[[fill_choice_big-387]][[image-2174]]","widgets":{"fill_choice_big-387":{"type":"fill_choice_big","options":["$93\\space500$","$93\\space300$","$93\\space450$"],"placeholder":0,"answer":0},"image-2174":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/crowded-1.svg","width":"300"}},"hints":["Find the number of children and teenagers: $$0.15\\cdot200\\space000=30\\space000\\space people$$ Find the number of adult residents: $$200\\space000-30\\space000=170\\space000\\space people$$ Find the number of adults who do not work: $$0.45\\cdot170\\space000=76\\space500\\space people$$ Calculate the number of working adults: $$170\\space000-76\\space500=93\\space500\\space people$$ $93\\space500$ adult residents work."]}]}

{"questions":[{"content":"The bank charges $12\\%$ per annum on the time deposit. The depositor deposited rubles into the account $3\\space000$. How many rubles will be in this account in a year if no operations, except for the accrual of interest, are carried out on the account?[[fill_choice_big-1]][[image-768]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$3\\space340$","$3\\space360$","$3\\space380$"],"placeholder":0,"answer":1},"image-768":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/bank.svg","width":"300"}},"hints":["Determine the amount of interest that accrues for the year: $$0.12\\cdot3\\space000=360\\space rubles$$ Find the total amount on the account in a year: $$3\\space000 +360 =3\\space360\\space rubles$$ After a year there will be $3\\space360$ rubles in the account."]},{"content":"The bank charges $21\\%$ per annum on the time deposit. The depositor deposited rubles into the account $11\\space000$. How many rubles will be in this account in a year if no operations, except for the accrual of interest, are carried out on the account?[[fill_choice_big-7]][[image-813]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$13\\space310$","$13\\space390$","$13\\space360$"],"placeholder":0,"answer":0},"image-813":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/bank2.svg","width":"300"}},"hints":["Determine the amount of interest that accrues for the year: $$0.21\\cdot11\\space000=2\\space310\\space rubles$$ Find the total amount on the account in a year: $$ 11\\space000+2\\space310=13\\space310\\space rubles$$ After a year there will be $13\\space310$ rubles in the account."]},{"content":"At the beginning of the year, the number of subscribers of the Vostok telephone company was $800$ thousand people, and at the end of the year there were $880$ thousand people. By what percentage did the number of subscribers of this company increase over the year?[[fill_choice_big-53]][[image-886]]","widgets":{"fill_choice_big-53":{"type":"fill_choice_big","options":["$10$","$20$","$30$"],"placeholder":0,"answer":0},"image-886":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2025/01/pic_1-01.svg","width":"300"}},"hints":["Determine how many thousand people the number of subscribers has increased by: $$880-800=80$$ Find what percentage this increase is from the initial number of subscribers: $$\\frac{80}{800}\\cdot100\\%=10\\%$$ The number of subscribers has increased by $10\\%.$"]},{"content":"At the beginning of the year, the number of subscribers of the Vostok telephone company was $700$ thousand people, and at the end of the year there were $840$ thousand people. By what percentage did the number of subscribers of this company increase over the year?[[fill_choice_big-170]][[image-939]]","widgets":{"fill_choice_big-170":{"type":"fill_choice_big","options":["$20$","$10$","$15$"],"placeholder":0,"answer":0},"image-939":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/05/lyudi-01.svg","width":"300"}},"hints":["Determine how many thousand people the number of subscribers has increased by: $$840-700=140$$ Find what percentage this increase is from the initial number of subscribers: $$\\frac{140}{700}\\cdot100\\%=20\\%$$ The number of subscribers has increased by $20\\%.$"]},{"content":"After the TV was marked down, its new price was $0.96$ of the old price. By what percentage did the price of the TV decrease as a result of the markdown?[[fill_choice_big-207]][[image-996]]","widgets":{"fill_choice_big-207":{"type":"fill_choice_big","options":["$4$","$5$","$6$"],"placeholder":0,"answer":0},"image-996":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/06/page-1.svg","width":"300"}},"hints":["The new price of the TV is $0.96$ from the old price, that is, $96\\%$. Find by what percentage the price decreased: $$100\\%-96\\%=4\\%$$The price of the TV decreased by $4\\%.$"]},{"content":"After the system unit was marked down, its new price was $0.87$ of the old price. By what percentage did the price of the system unit decrease as a result of markdown?[[fill_choice_big-339]][[image-1057]]","widgets":{"fill_choice_big-339":{"type":"fill_choice_big","options":["$13$","$17$","$15$"],"placeholder":0,"answer":0},"image-1057":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/shop-assistant-1.svg","width":"300"}},"hints":["The new price of the system unit is $0.87$ from the old price, that is, $87\\%.$ Find by how many percent the price has decreased: $$100\\%-87\\%=13\\%$$The price of the system unit has decreased by $13\\%.$"]},{"content":"To prepare minced meat, we took beef and lamb in relation to $1 : 9$, respectively. What percentage of minced meat is lamb?[[fill_choice_big-402]][[image-1122]]","widgets":{"fill_choice_big-402":{"type":"fill_choice_big","options":["$90$","$80$","$70$"],"placeholder":0,"answer":0},"image-1122":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/12/obrazavr_myasnoj-prilavok.svg","width":"300"}},"hints":["Let us denote the share of beef as $1$ part, and the share of lamb as $9$ parts. Total number of parts - $10.$<br />Determine what percentage is lamb: $$\\frac{9}{10}\\cdot100\\%=90\\%$$ Lamb is $90\\%$ in minced meat."]},{"content":"The store gives a discount to pensioners. A loaf of bread costs $20$ rubles in the store, and the pensioner paid $19$ rubles $40$ kopecks for it. What percentage was the discount for a pensioner?[[fill_choice_big-525]][[image-1191]]","widgets":{"fill_choice_big-525":{"type":"fill_choice_big","options":["$3$","$5$","$1$"],"placeholder":0,"answer":0},"image-1191":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/hleb-01.svg","width":"300"}},"hints":["Determine the discount amount: $$20-19.40=0.60\\space rubles$$ Find what percentage the discount is from the original price: $$\\frac{0.60}{20}\\cdot100\\%=3\\%$$ The discount for a pensioner was $3\\%.$"]},{"content":"The store gives a discount to pensioners. Milk costs $60$ rubles in the store, and the pensioner paid $48$ rubles for it. What percentage was the discount for a pensioner?[[fill_choice_big-649]][[image-1246]]","widgets":{"fill_choice_big-649":{"type":"fill_choice_big","options":["$20$","$30$","$40$"],"placeholder":0,"answer":0},"image-1246":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/09/milk.svg","width":"300"}},"hints":["Determine the discount amount: $$60-48=12\\space rubles$$ Find what percentage the discount is from the original price: $$\\frac{12}{60}\\cdot100\\%=20\\%$$ The discount for a pensioner was $20\\%.$"]},{"content":"A children's goods store buys rattles at a wholesale price of $120$ rubles per piece and sells them at a premium $25\\%.$ How many rubles will $3$ such rattles purchased in this store cost? [[fill_choice_big-75]][[image-1342]]","widgets":{"fill_choice_big-75":{"type":"fill_choice_big","options":["$450$","$400$","$460$"],"placeholder":0,"answer":0},"image-1342":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/the-ball-is-at-the-wall.svg","width":"300"}},"hints":["Find the markup for one rattle: $$0.25\\cdot120=30\\space rubles$$ Determine the retail price of one rattle: $$120+30=150\\space rubles$$ Find the cost of three rattles: $$3\\cdot150=450\\space rubles$$ Three rattles will cost $450$ rubles."]}]}

{"questions":[{"content":"A bottle of shampoo costs $160$ rubles. What is the largest number of bottles you can buy for $1\\space000$ rubles during a sale, when the discount is $25\\% ?$[[fill_choice_big-1]][[image-41]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$7$","$8$","$6$"],"placeholder":0,"answer":1},"image-41":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/dush-vanna-moetsya-v-vannoj-2.svg","width":"300"}},"hints":["The discount is $25\\%,$, which means the buyer pays $75\\%$ from the original price: $$160\\cdot0.75=120 \\space rubles$$ Divide the total budget by the price of one bottle with a discount: $$\\frac{1\\space000}{120}=8.3$$ Round down to the nearest whole number. It will be possible to buy $8$ bottles of shampoo."]},{"content":"The winners of the city Olympiad in mathematics were $25$ students, which amounted to $5\\%$ of the number of participants. How many people participated<br />in the Olympics?[[fill_choice_big-37]][[image-86]]","widgets":{"fill_choice_big-37":{"type":"fill_choice_big","options":["$500$","$750$","$1\\space500$"],"placeholder":0,"answer":0},"image-86":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/maths-1.svg","width":"300"}},"hints":["Convert the percentages into decimal fractions and calculate the value: $$x=\\frac{25}{0.05}=500$$ $500$ people participated in the Olympiad.<br /><br />"]},{"content":"A pack of butter costs $75$ rubles. The store gives a discount to pensioners $20\\%.$ How many rubles does a stick of butter cost for a pensioner?[[fill_choice_big-50]][[image-135]]","widgets":{"fill_choice_big-50":{"type":"fill_choice_big","options":["$50$","$60$","$80$"],"placeholder":0,"answer":1},"image-135":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/butter-1.svg","width":"300"}},"hints":["Calculate the discount amount. <br />The discount is $20\\%$ from the original price: $$75\\cdot0.20=15\\space rubles$$ Determine the price of a stick of butter for a pensioner.<br />Subtract the discount from the original price: $$75-15=60\\space rubles$$ A stick of butter for a pensioner will cost $60\\space$ rubles."]},{"content":"A pack of butter costs $90$ rubles. The store offers a discount $30\\%$ to pensioners. How many rubles does a stick of butter cost for a pensioner?[[fill_choice_big-116]][[image-188]]","widgets":{"fill_choice_big-116":{"type":"fill_choice_big","options":["$63$","$66$","$67$"],"placeholder":0,"answer":0},"image-188":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2021/12/babushka-i-dedushka-1.svg","width":"300"}},"hints":["Calculate the discount amount.<br />The discount is $30\\%$ from the original price: $$90\\cdot0.30=27\\space rubles$$ Determine the price of a stick of butter for a pensioner.<br />Subtract the discount from the original price: $$90-27=63\\space rubles$$A stick of butter for a pensioner will cost $63\\space$ rubles."]},{"content":"During the sale period, the store reduced prices twice: the first time by $10\\%,$ and the second by $25\\%.$ How many rubles did the kettle cost after the second price reduction, if before the start of the sale it cost $1\\space600$ rubles? [[fill_choice_big-245]][[image-231]]","widgets":{"fill_choice_big-245":{"type":"fill_choice_big","options":["$1\\space080$","$1\\space060$","$1\\space040$"],"placeholder":0,"answer":0},"image-231":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/chajnik.svg","width":"300"}},"hints":["The first reduction is $10\\%,$, which means the price after the first reduction will be $90\\%$ from the original: $$1\\space600\\cdot0.90=1\\space440\\space rubles$$ The second reduction is $25\\%,$, which means the price after the second reduction will be $75\\%$ from the price after the first reduction: $$1\\space440\\cdot0.75=1\\space080\\space rubles$$The price of the kettle after the second reduction is $1\\space080\\space$ rubles."]},{"content":"The monthly fee for the telephone is $250$ rubles. Next year it will increase by $2\\%.$ How many rubles will the monthly payment for the phone next year be?[[fill_choice_big-361]][[image-307]]","widgets":{"fill_choice_big-361":{"type":"fill_choice_big","options":["$255$","$260$","$275$"],"placeholder":0,"answer":0},"image-307":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/mobile_phone-1.svg","width":"300"}},"hints":["Calculate the amount of increase.<br />The increase is $2\\%$ from the current fee: $$250\\cdot0.02=5\\space rubles$$ Determine a new monthly fee.<br />Add the increase amount to the current fee: $$250+5=255\\space rubles$$ The monthly fee for the phone next year will be $255$ rubles."]},{"content":"Of $3\\space000$ school graduates of the city $90\\%$ correctly solved the problem $№\\space1.$ How many school graduates of this city correctly solved the problem $№\\space1?$[[fill_choice_big-457]][[image-388]]","widgets":{"fill_choice_big-457":{"type":"fill_choice_big","options":["$2\\space700$","$2\\space300$","$2\\space900$"],"placeholder":0,"answer":0},"image-388":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/02/student-uchenik.svg","width":"300"}},"hints":["Calculate the number of graduates who correctly solved the problem $№\\space1.$<br />$90\\%$ of the total number of graduates: $$3\\space000\\cdot0.90=2\\space700$$ The number of graduates who solved the problem $№\\space1$ correctly is $2\\space700$ people."]},{"content":"Of $1\\space500$ school graduates of the city $30\\%$ correctly solved the problem $№\\space3.$ How many school graduates of this city correctly solved the problem $№\\space3?$[[fill_choice_big-605]][[image-457]]","widgets":{"fill_choice_big-605":{"type":"fill_choice_big","options":["$450$","$500$","$400$"],"placeholder":0,"answer":0},"image-457":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/graduated.svg","width":"300"}},"hints":["Calculate the number of graduates who correctly solved the problem $№\\space3$.<br />$30\\%$ of the total number of graduates: $$1\\space500\\cdot0.30=450$$ The number of graduates who solved the problem $№\\space3$ correctly is $450$ people."]},{"content":"A set of towels that cost $200$ rubles is sold at a discount $13\\%.$ How many rubles do two sets of towels cost at a discount? [[fill_choice_big-420]][[image-530]]","widgets":{"fill_choice_big-420":{"type":"fill_choice_big","options":["$348$","$346$","$358$"],"placeholder":0,"answer":0},"image-530":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/polotencze.svg","width":"300"}},"hints":["We will calculate the cost of one set at a discount.<br />The discount is $13\\%,$, which means the buyer pays $87\\%$ from the original price: $$200\\cdot0.87=174\\space rubles$$ Determine the cost of two sets with a discount. $$174\\cdot2=348\\space rubles$$ Two sets of towels with a discount will cost $348\\space$ rubles.<br />"]},{"content":"The city budget is $19$ million rubles, and the expenses for one of its items amounted to $15\\%.$ How many million rubles were spent on this budget item?[[fill_choice_big-41]][[image-607]]","widgets":{"fill_choice_big-41":{"type":"fill_choice_big","options":["$2.85$","$2.95$","$2.75$"],"placeholder":0,"answer":0},"image-607":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2024/01/gorod-01.svg","width":"300"}},"hints":["Calculate the amount of expenses per budget item.<br />$15\\%$ of the total budget: $$19\\cdot0.15=2.85$$ The expenditure on this budget item amounted to $2.85$ million rubles."]}]}