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.
 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.
 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. 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, crossmultiply, set the crossproducts equal to each other, and solve as shown below.
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.
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, crossmultiply 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.
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.
The price of the book is $26.50.
More practice problems on percents word problems can be found at:
 Percents Word Problems Practice Questions Set 1
 Percents Word Problems Practice Questions Set 2 (You are here)
 Percents Word Problems Practice Questions Set 3
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