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.
- Mr. Pelicas took his family out to dinner. The bill was $65.00. He would like to leave a 17% tip. How much should he leave?
- $17
- $3.25
- $11.05
- $16.25
- The Daily News reported that 54% of people surveyed said that they would vote for Larry Salva for mayor. Based on the survey results, if 23,500 people vote in the election, how many people are expected to vote for Mr. Salva?
- 12,690
- 4,350
- 10,810
- 18,100
- Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price?
- 130%
- 60%
- 70%
- 97%
- A pair of mittens has been discounted 13.5%. The original price of the mittens was $10. What is the new price?
- $8.80
- $8.65
- $7.50
- $9.87
- John's youth group is trying to raise $1,500 at a car wash. So far, they have raised $525. What percent of their goal have they raised?
- 35%
- 52%
- 3%
- 28%
- The freshman class is participating in a fundraiser. Their goal is to raise $5,000. After the first two days of the fundraiser, they have raised 32% of their goal. How many dollars did they raise the first two days?
- $160
- $32
- $1,600
- $3,400
- 1,152 out of 3,600 people surveyed said that they work more than 40 hours per week. What percent of the people surveyed said that they work more than 40 hours per week?
- 32%
- 3.1%
- 40%
- 24%
- Peter was 60 inches tall on his thirteenth birthday. By the time he turned 15, his height had increased 15%. How tall was Peter when he turned 15?
- 75 inches
- 69 inches
- 72 inches
- 71 inches
- Laura paid $17 for a pair of jeans. The ticketed price was 20% off the original price plus the sign on the rack said, "Take an additional 15% off the ticketed price." What was the original price of the jeans?
- $30
- $28
- $25
- $21
- The 6% sales tax on a basket was $0.72. What was the price of the basket?
- $12
- $43.20
- $17
- $24.50
- What percent of the figure below is shaded?
- 50%
- 65%
- 75%
- 80%
- Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. When the bill came, Melisa added a 15% tip of $42. Jennifer said that the service was wonderful and they should leave a 20% tip instead. How much is a 20% tip?
- $56
- $45
- $47
- $60
- The Hamden Town Manager wants to know what percent of the snow removal budget has already been spent. The budget for snow removal is $130,000. It has been an exceptionally snowy year, and they have already spent $100,000 for snow removal. What percent of the budget has already been spent? (round to the nearest percent)
- 30%
- 70%
- 72%
- 77%
- A real estate agent makes a 1.5% commission on her sales. What is her commission if she sells a $359,000 house?
- $53,850
- $5,385
- $23,933
- $1,500
- The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $42, what price tag will he put on the item?
- $84
- $83.50
- $65
- $88.20
- Michelle purchased a vacation home with her sisters. Michelle has $125,000 invested in the property, which is worth $400,000. What percent of the property does Michelle own?
- 3.2%
- 43%
- 31.25%
- 26.5%
- Kyra's weekly wages are $895. A Social Security tax of 7.51% and a State Disability Insurance of 1.2% are taken out of her wages. What is her weekly paycheck, assuming there are no other deductions?
- $827.79
- $884.26
- $962.21
- $817.05
- Oscar's Oil Company gives customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill within 10 days?
- $8.90
- $5.00
- $17.80
- $14.60
- Josephine is on an 1,800 calorie per day diet. She tries to keep her intake of fat to no more than 30% of her total calories. Based on an 1,800 calorie a day diet, what is the maximum number of calories that Josephine should consume from fats per day to stay within her goal?
- 600
- 640
- 580
- 540
- A family may deduct 24% of their childcare expenses from their income tax owed. If a family had $1,345 in childcare expenses, how much can they deduct?
- $1,022.20
- $345.00
- $322.80
- $789.70
- A factory that is working at 90% capacity is shipping 450 cars per week. If the factory works at 100% capacity, how many cars can it ship per week?
- 650
- 500
- 495
- 405
- Sales increased by only % last month. If the sales from the previous month were $152,850, what were last month's sales?
- $229,275.00
- $153,614.25
- $152,849.05
- $151,397.92
- Laura is planning her wedding. She expects 220 people to attend the wedding, but she has been told that approximately 5% typically don't show. About how many people should she expect not to show?
- 46
- 5
- 11
- 23
Answers
- c. Find 17% by multiplying $65 by the decimal equivalent of 17% (0.17); $65 × 0.17 = $11.05. The tip is $11.05.
- a. Find 54% of 23,500 by multiplying 23,500 by the decimal equivalent of 54% (0.54); 23,500 × 0.54 = 12,690; 12,690 people are expected to vote for Mr. Salva.
- c. The original price of the bike is 100%. If the sale takes 30% off the price, it will leave 70% of the original price (100% – 30% = 70%).
- b. Find 13.5% of $10 and subtract it from $10. Find 13.5% of $10 by multiplying $10 by the decimal equivalent of 13.5% (0.135); $10 × 0.135 = $1.35; $1.35 is taken off the price of the mittens. Subtract $1.35 from $10 to find the sale price; $10 – $1.35 = $8.65. The sale price is $8.65.
Another way to compute the sale price is to find what percent is left after taking the discount. The original price was 100% and 13.5% is taken off; 86.5% is left (100% – 13.5% = 86.5%). Find 86.5% of the original cost by multiplying $10 by the decimal equivalent of 86.5% (0.865); $10 × 0.865 = $8.65.
- a. Use a proportion to solve the problem; The Whole is $1,500 and the part is $525. You are looking for the %, so it is x. To solve the proportion, cross-multiply, set the cross-products equal to each other, and solve as shown below.
They have raised 35% of the goal.
Another way to find the percent is to divide the part by the Whole, which gives you a decimal. Convert the decimal into a percent by multiplying by 100 (move the decimal point two places to the right);
- c. Find 32% of $5,000 by multiplying $5,000 by the decimal equivalent of 32% (0.32); $5,000 × 0.32 = $1,600.
- a. Divide the part by the Whole; 1,152 ÷ 3,600 = 0.32. Change the decimal to a percent by multiplying by 100 (move the decimal point two places to the right); 32% of the people surveyed said that they work more than 40 hours a week.
Another way to find the answer is to use a proportion; The part is 1,152, the Whole is 3,600, and the % is x. To solve the proportion, cross-multiply, set the cross-products equal to each other, and solve as shown below.
- b. Find 15% of 60 inches and add it to 60 inches. Find 15% by multiplying 60 by the decimal equivalent of 15% (0.15); 60 × 0.15 = 9. Add 9 inches to 60 inches to get 69 inches.
- c. Call the original price of the jeans x. First 20% is deducted from the original cost (the original cost is 100%); 80% of the original cost is left (100% – 20% = 80%); 80% of x is 0.80x. The cost of the jeans after the first discount is 0.80x. This price is then discounted 15%. Remember 15% is taken off the discounted price; 85% of the discounted price is left. Multiply the discounted price by 0.85 to find the price of the jeans after the second discount; (0.85)(0.80x) is the cost of the jeans after both discounts. We are told that this price is $17. Set the two expressions for the cost of the jeans equal to each other (0.85)(0.80x) = $17 and solve for x (the original cost of the jeans).
The original price of the jeans was $25.
- a. Use a proportion to solve the problem; The whole is the price of the basket (which is unknown, so call it x), the part is the tax of $0.72, and the percentage is 5. The proportion is Solve the proportion by cross-multiplying, setting the cross-products equal to each other, and solving as shown below.
The price of the basket was $12.
- c. Break the rectangle into eighths as shown below. The shaded part is
- a. To find 20%, add 5% to 15%. Since 15% is known to be $42, 5% can be found by dividing $42 by 3 (15% ÷ 3 = 5%); $42 ÷ 3 = $14. To find 20%, add the 5% ($14) to the 15% ($42); $14 + $42 = $56; 20% is $56.
- d. Use a proportion to solve the problem; The part is $100,000, the whole is $130,000, and the percentage is x because it is unknown; To solve the proportion, cross-multiply, set the cross-products equal to each other, and solve as shown below.
77% of the budget has been spent.
- b. Multiply $359,000 by the decimal equivalent of 1.5% (0.015) to find her commission; $359,000 × 0.015 = $5,385; $5,385 is the commission.
A common mistake is to use 0.15 for the decimal equivalent of 1.5%; 0.15 is equivalent to 15%. Remember, to find the decimal equivalent of a percent, move the decimal point two places to the left.
- d. To find the price he sells it for, add the mark-up to his cost ($42). The mark-up is 110%. To find 110% of his cost, multiply by the decimal equivalent of 110% (1.10); $42 × 1.10 = $46.20. The mark-up is $46.20. Add the mark-up to his cost to find the price the vase sells for; $46.20 + $42.00 = $88.20.
- c. Use a proportion to solve the problem; The part is $125,000 (the part Michelle owns), the whole is $400,000 (the whole value of the house), and the percentage is x because it is unknown.
To solve the proportion, cross-multiply, set the cross-products equal to each other, and solve as shown below.
Michelle owns 31.25% of the vacation home.
- d. Find the Social Security tax and the State Disability Insurance, and then subtract the answers from Kyra's weekly wages. To find 7.51% of $895, multiply by the decimal equivalent of 7.51% (0.0751); $895 × 0.0751 = $67.21 (rounded to the nearest cent). Next, find 1.2% of her wages by multiplying by the decimal equivalent of 1.2% (0.012); $895 × 0.012 = $10.74. Subtract $67.21 and $10.74 from Kyra's weekly wages of $895 to find her weekly paycheck; $895 – $67.21 – $10.74 = $817.05. Her weekly paycheck is $817.05.
- a. Find 5% of the bill by multiplying by the decimal equivalent of 5% (0.05); $178 × 0.05 = $8.90. They will save $8.90.
A common mistake is to use 0.5 instead of 0.05 for 5%; 0.5 is 50%.
- d. Find 30% of 1,800 by multiplying by the decimal equivalent of 30% (0.30); 1,800 × 0.30 = 540. The maximum number of calories from fats per day is 540.
- c. Find 24% of $1,345 by multiplying by the decimal equivalent of 24% (0.24); $1,345 × 0.24 = $322.80. $322.80 can be deducted.
- b. Use the proportion You are looking for the whole (100% is the whole capacity of the plant). The part you know is 450 and it is 90% of the whole; To solve the proportion, cross multiply, set the cross-products equal to each other, and solve as shown below.
100% capacity is 500 cars.
Another way to look at the problem is to find 10% and multiply it by 10 to get 100%. Given 90%, divide by 9 to find 10%; 450 ÷9 = 50. Multiply 10% (50) by 10 to find 100%; 50 × 10 = 500.
- b. Multiply by the decimal equivalent of % (0.005) to find the amount of increase; $152,850 × 0.005 = $764.25. This is how much sales increased. To find the actual amount of sales, add the increase to last month's total; $152,850 + $764.25 = $153,614.25.
A common mistake is to use 0.5 (50%) or 0.05 (5%) for%. Rewrite % as 0.5%. To find the decimal equivalent, move the decimal point two places to the left. This yields 0.005.
- c.Find 5% of 220 by multiplying 220 by the decimal equivalent of 5% (0.05); 220 × 0.05 = 11 people.
A common mistake is to use 0.5 for 5%; 0.5 is actually 50%.
More practice problems on percents word problems can be found at:
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