Percent Problems in Context
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ISEE Middle Level: Quantitative Reasoning › Percent Problems in Context
A recipe for a smoothie requires 20 ounces of liquid. 75% of the liquid is yogurt. If the rest of the liquid is juice, how many ounces of juice are required?
5
10
15
25
Explanation
If 75% of the liquid is yogurt, then the remaining percentage must be juice. The percentage of juice is \(100% - 75% = 25%\). To find the amount of juice, calculate 25% of the total liquid volume: \(0.25 \times 20 = 5\) ounces.
A club has 15 members who are in 7th grade and 10 members who are in 8th grade. What percentage of the club members are in 7th grade?
15%
40%
60%
67%
Explanation
First, find the total number of members in the club: \(15 + 10 = 25\). Next, calculate the percentage of members who are in 7th grade by dividing the number of 7th graders by the total number of members and multiplying by 100: \(\frac{15}{25} \times 100% = 0.60 \times 100% = 60%\).
Sarah deposits $600 into a savings account that earns 2.5% simple annual interest. If she does not make any other deposits or withdrawals, how much interest will she have earned after 3 years?
$4.50
$15.00
$45.00
$645.00
Explanation
Simple interest is calculated using the formula I = Prt, where I is interest, P is principal, r is the rate, and t is time. First, find the interest for one year: \($600 \times 0.025 = $15\). Then, multiply by the number of years to find the total interest: \($15 \times 3 = $45\).
A fundraising event raised a total of $5,000. 30% of the money will be used for administrative costs. The remaining money will be split equally among 4 charities. How much money will each charity receive?
$1,250
$3,500
$1,500
$875
Explanation
First, calculate the amount of money remaining after administrative costs. If 30% is used for costs, then 70% remains for charities. The amount for charities is \(0.70 \times $5,000 = $3,500\). This amount is split equally among 4 charities, so each charity receives \($3,500 \div 4 = $875\).
A test has two sections. A student answered 80% of the 30 questions in the first section correctly. If the student scored 70% on the entire 50-question test, what percentage of the 20 questions in the second section did the student answer correctly?
55%
60%
65%
75%
Explanation
First, find the number of questions answered correctly in section 1: \(30 \times 0.80 = 24\). Next, find the total number of questions answered correctly on the whole test: \(50 \times 0.70 = 35\). The number of questions answered correctly in section 2 is the difference: \(35 - 24 = 11\). Finally, find the percentage for section 2, which has 20 questions: \(\frac{11}{20} \times 100% = 55%\).
A video game originally priced at $50 is on sale for 20% off. A week later, the store offers an additional 10% off the sale price. What is the final price of the game?
$35.00
$36.00
$40.00
$45.00
Explanation
First, calculate the initial sale price. A 20% discount on $50 is \(0.20 \times 50 = $10\). The sale price is \($50 - $10 = $40\). Next, calculate the additional 10% discount on the sale price. A 10% discount on $40 is \(0.10 \times 40 = $4\). The final price is \($40 - $4 = $36\).
A jacket is on sale for $60 after a 25% discount. What was the original price of the jacket?
$45.00
$75.00
$80.00
$90.00
Explanation
The sale price of $60 represents 100% - 25% = 75% of the original price. Let P be the original price. The equation is \(0.75 \times P = $60\). To find the original price, divide the sale price by 0.75: \(P = $60 \div 0.75 = $80\).
A family's dinner bill is $120. They want to leave a 20% tip on the bill before tax is added. The sales tax is 10% of the bill. What is the total amount they will pay?
$132.00
$144.00
$156.00
$158.40
Explanation
First, calculate the tip: 20% of $120 is \(0.20 \times 120 = $24\). Next, calculate the sales tax: 10% of $120 is \(0.10 \times 120 = $12\). The total amount is the sum of the bill, the tip, and the tax: \($120 + $24 + $12 = $156\).
A school library has 1,200 books. 45% of the books are fiction. Of the fiction books, 20% are science fiction. How many science fiction books are in the library?
108
240
540
780
Explanation
First, find the number of fiction books: \(1200 \times 0.45 = 540\). Then, find the number of science fiction books, which is 20% of the fiction books: \(540 \times 0.20 = 108\).
The population of a town was 8,000 in 2020. By 2021, the population had increased by 5%. What was the population of the town in 2021?
8,400
8,040
400
12,000
Explanation
First, calculate the increase in population: 5% of 8,000 is \(0.05 \times 8000 = 400\). Then, add this increase to the original population: \(8000 + 400 = 8,400\). Alternatively, a 5% increase means the new population is 105% of the original: \(8000 \times 1.05 = 8,400\).