Percents Word Problems
Percentages have many everyday uses, from figuring out the tip in restaurant to understanding interest rates. This set of practice problems will give you practice in solving word problems that involve percents.
- There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High?
- 180
- 36
- 165
- 205
- Kim is a medical supplies salesperson. Each month she receives a 5% commission on all her sales of medical supplies up to $20,000 and 8.5% on her total sales over $20,000. Her total commission for May was $3,975. What were her sales for the month of May?
- $79,500
- $64,250
- $46,764
- $55,000
- In the school play, 64% of the students are boys. If there are 75 students in the play, how many are boys?
- 64
- 45
- 27
- 48
- Christie purchased a scarf marked $15.50 and gloves marked $5.50. Both items were on sale for 20% off the marked price. Christie paid 5% sales tax on her purchase. How much did she spend?
- $25.20
- $16.80
- $26.46
- $17.64
- Last year, a math textbook cost $54. This year the cost is 107% of what it was last year. What is this year's cost?
- $59.78
- $57.78
- $61.00
- $50.22
- Larry earned $32,000 per year. Then he received a 3% raise. What is Larry's salary after the raise?
- $33,040
- $35,000
- $32,140
- $32,960
- Bill spent 50% of his savings on school supplies, then he spent 50% of what was left on lunch. If he had $8 left after lunch, how much did he have in savings at the beginning?
- $32
- $16
- $30
- $18
- A coat that costs $72 is marked up 22%. What is the new price of the coat?
- $78.22
- $96.14
- $56.16
- $87.84
- Kristen earns $550 each week after taxes. She deposits 10% of her income in a savings account and 7% in a retirement fund. How much does Kristen have left after the money is taken out for her savings account and retirement fund?
- $505.25
- $435.50
- $533.00
- $456.50
- Coastal Cable had 1,440,000 customers in January of 2002. During the first half of 2002 the company launched a huge advertising campaign. By the end of 2002 they had 1,800,000 customers. What is the percent of increase?
- 36%
- 21%
- 20%
- 25%
- The price of heating oil rose from $1.70 per gallon to $2.38 per gallon. What is the percent of increase?
- 40%
- 33%
- 29%
- 38%
- 450 girls were surveyed about their favorite sport: 24% said that basketball is their favorite sport, 13% said that ice hockey is their favorite sport, and 41% said that softball is their favorite sport. The remaining girls said that field hockey is their favorite sport. What percent of the girls surveyed said that field hockey is their favorite sport?
- 37%
- 22%
- 78%
- 35%
- At Yale New Haven Hospital, 25% of babies born weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh between 6 and 8.5 pounds?
- 22%
- 24%
- 53%
- 2.5%
- An $80.00 coat is marked down 20%. It does not sell, so the shop owner marks it down an additional 15%. What is the new price of the coat?
- $64.00
- $68.60
- $52.00
- $54.40
- of the soda purchased at the football game was cola. What percentage of the soda purchased was cola?
- 60%
- 40%
- 30%
- 70%
- In a recent survey of 700 people, 18% said that red was their favorite color. How many people said that red was their favorite color?
- 18
- 88
- 125
- 126
- In Kimmi's fourth grade class, 8 out of the 20 students walk to school. What percent of the students in her class walk to school?
- 40%
- 50%
- 45%
- 35%
- In Daniel's fifth grade class, 37.5% of the 24 students walk to school. Onethird of the walkers got a ride to school today from their parents. How many walkers got a ride to school from their parents today?
- 9
- 12
- 2
- 3
- Lindsay purchased a pocketbook for $45 and a pair of shoes for $55. The sales tax on the items was 6%. How much sales tax did she pay?
- $2.70
- $3.30
- $6.00
- $6.60
- Wendy bought a book and the sales tax on the book was $2.12. If the sales tax is 8%, what was the price of the book?
- $26.50
- $16.96
- $24.76
- $265.00
Answers
- a. Use the proportion Part is the number of female teachers (81). Whole is what we are looking for; call it x; the % is 45; Cross multiply; (81)(100) = 45x. Divide both sides by 45 to solve for x;
- d. Kim sold over $20,000 in May. She received a 5% commission on the first $20,000 of sales. To find 5%, multiply by the decimal equivalent of 5% (0.05); $20,000 × 0.05 = $1,000. Since her total commission was $3,975, $3,975 – $1,000 = $2,975 is the amount of commission she earned on her sales over $20,000. $2,975 is 8.5% of her sales over $20,000. To find the amount of her sales over $20,000, use a proportion; Part is $2,975, and whole is what we are looking for, so let's call it x. The % is 8.5; To solve for x, cross multiply; (2,975)(100) = 8.5x. Divide both sides by 8.5 to solve; x = $35,000. Her sales over $20,000 were $35,000. Her total sales were $55,000 ($20,000 + $35,000).]
- d. To find 64% of 75, multiply 75 by the decimal equivalent of 64% (0.64); 75 × 0.64 = 48. If you chose c, you found the number of girls.
- d. First, find the sale price of the scarf and the gloves. They are both 20% off, which means that Christie paid 80% of the original price (100% – 20% = 80%). To find 80% of each price, multiply the price by the decimal equivalent of 80% (0.80); $15.50 × 0.80 = $12.40. $5.50 × 0.80 = $4.40. Together the two items cost $16.80 ($12.40 + $4.40 = $16.80). There is 5% sales tax on the total price. To find 5% of $16.80, multiply $16.80 by the decimal equivalent of 5% (0.05); $16.80 × 0.05 = $0.84. The tax is $0.84. Christie paid a total of $17.64 ($16.80 + $0.84 = $17.64).]
- b. To find 107% of $54, multiply $54 by the decimal equivalent of 107% (1.07); $54 × 1.07 = $57.78. If you chose d, you found what the cost of the book would be if it was 7% LESS next year.
- a. If Larry earns a 3% (or 3.25%) raise, he will earn 103.25% of his original salary. To find 103.35% of $32,000, multiply $32,000 by the decimal equivalent of 103.25% (1.0325); $32,000 × 1.0325 = $33,040. If you chose d, you found his salary with a 3% raise when multiplying by 1.03 or 0.03 and then adding that answer to his original salary.
- a. Work backwards to find the answer. After lunch Bill had $8. He had spent 50% (or ) of what he had on lunch and 50% is what is left. Since $8 is 50% of what he had before lunch, he had $16 before lunch. Using the same reasoning, $16 is 50% of what he had before buying school supplies. Therefore, he had $32 when he began shopping.
- d. If a coat is marked up 22%, it is 122% of its original cost (100% + 22% = 122%). To find 122% of the original cost, multiply $72 by the decimal equivalent of 122% (1.22); $72 × 1.22 = $87.84.
- d. Kristen has a total of 17% taken out of her check. Therefore, she is left with 83% of what she started with (100% – 17% = 83%). To find 83% of $550, multiply $550 by the decimal equivalent of 83%; $550 × 0.83 = $456.50.
- d. Coastal Cable gained a total of 360,000 customers (1,800,000 – 1,440,000 = 360,000). To find out what percent of the original number of customers 360,000 represents, divide 360,000 by 1,440,000; 360,000 ÷ 1,440,000 = 0.25; 0.25 is equivalent to 25%. If you chose c, you found the percent of increase in relation to the new number of customers (1,800,000) rather than the original number of customers (1,440,000).
- a. The price of heating oil rose $0.68 ($2.38 – $1.70 = $0.68). To find the percent of increase, divide $0.68 by the original cost of $1.70; $0.68 ÷ $1.70 = 0.4; 0.4 is equivalent to 40%. If you chose c, you found the percent of increase in relation to the new price ($2.38) rather than the original price ($1.70).
- b. The percents must add to 100%; 24% + 13% + 41% = 78%. If 78% of the girls surveyed have been accounted for, the remainder of the girls must have said that field hockey is their favorite sport. To find the percent that said field hockey is their favorite sport, subtract 78% from 100%; 100% – 78% = 22%; 22% of the girls said that field hockey is their favorite sport.
- c. 78% weigh less than 8.5 pounds, but you must subtract the 25% that are below 6 pounds; 78% – 25% = 53%. 53% of the babies weigh between 6 and 8.5 pounds.
- d. Find 20% of the original price of the coat and subtract it from the original price. To find 20%, multiply by 0.20; $80 × 0.20 = $16. Take $16 off the original price; $80 – $16 = $64. The first sale price is $64. Take 15% off this using the same method; $64 × 0.15 = $9.60; $64 – $9.60 = $54.40. The new price of the coat is $54.40.
Another way of solving this problem is to look at the percent that is left after the discount has been taken. For example, if 20% is taken off, 80% is left (100% – 20%). Therefore, 80% of the original price is $80 × 0.80 = $64. If 15% is taken off this price, 85% is left; $64 × 0.85 = $54.40. This method eliminates the extra step of subtracting.
- a. Change the fraction to a decimal by dividing the numerator by the denominator (top ÷ bottom); 3 ÷ 5 = 0.6. Change 0.6 to a percent by multiplying by 100; 0.6 × 100 = 60%. Recall that multiplying by 100 means that the decimal point is moved two places to the right.
- d. Find 18% of 700 by multiplying 700 by the decimal equivalent of 18% (0.18); 700 × 0.18 = 126; 126 people said that red is their favorite color. Another way of looking at this problem is to recall that 18% means "18 out of 100." Since 700 is 7 times 100, multiply 18 by 7 to find the number of people out of 700 who said red was their favorite color; 18 × 7 = 126.
- a. Write the relationship as a fraction; Find the decimal equivalent by dividing the numerator by the denominator (top ÷ bottom); 8 ÷ 20 = 0.4. Change 0.4 to a percent by multiplying by 100; 0.4 × 100 = 40%. Recall that multiplying by 100 means that the decimal point is moved two places to the right.
Another way to look at this problem is using a proportion; You are looking for the percent, so that will be the variable; To solve the proportion, cross-multiply and set the answers equal to each other; (8)(100) = 20x. Solve for x by dividing both sides by 20.
40% of the students are walkers.
- d. First, find the number of walkers and then find one third of that number. Find 37.5% of 24 by multiplying 24 by the decimal equivalent of 37.5%. To find the decimal equivalent, move the decimal point two places to the left; 37.5% = 0.375. Now, multiply 24 × 0.375 = 9. Find one third of 9 by dividing 9 by 3; 9 ÷ 3 = 3. Three walkers got rides.
- c. Find the price of the two items together (without tax); $45 + $55 = $100. Next, find 6% of $100. You can multiply $100 by 0.06, but it is easier to realize that 6% means "6 out of 100," so 6% of $100 is $6. The sales tax is $6.
A common mistake is to use 0.6 for 6% instead of 0.06; 0.6 is 60%. To find the decimal equivalent of a percent, you must move the decimal point two places to the left.
- a. A proportion can be used to solve this problem; In this example, the part is the tax, the % is 8, and the Whole is x. To solve the proportion, cross-multiply, set the cross-products equal to each other, and solve as shown below.
The price of the book is $26.50.
More practice problems on percents word problems can be found at:
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