Percentages Practice Problems: GED Math

Answers

1. d.   One method of solution is to set up a proportion: part/whole = percent/100. The whole is 350, and the part is what is being requested in the problem. Substitute the given information: . Cross multiply to get 350 × 57 = n × 100, and then multiply 350 times 57: 19,950 = n × 100. Divide 19,950 by 100 to get 199.50 or the equivalent 199.5.
2. c.   Set up an equation, recalling that of means multiply and is means equals; make a straight translation using the variable p for percent. p × 200 = 68. Divide both sides by 200 to get p = 0.34. This is the answer as a decimal. Change this answer to a percent by multiplying by 100 to get 34%.
3. b.   Set up a proportion: . In the problem, 19 is the part, 76 is the percent, and the whole is what you need to calculate. Cross multiply to get n × 76 = 19 × 100. Multiply: n × 76 = 1,900. Now divide 1,900 by 76 to get 25.
4. b.   Two out of every five indicates a ratio, so use the proportion: . Cross multiply to get 5 × p = 2 × 100. Multiply: 5p = 200. Now divide both sides by 5 to get p = 40%.
5. e.   This is a multistep problem, because the sale percentage is a percent decrease, and the sales tax is a percent increase. There are several methods to solve this problem. Remember that 35% is 0.35 written as a decimal. Set up the equation: discount = percent × original, or d = 0.35 × $89. Multiply to get the discount, which is $31.15. The sale price is thus $89.00 – $31.15 = $57.85. The sales tax is then calculated based on this sale price: sales tax = percent × sale price. The tax will be t = 0.06 × $57.85, or t = $3.47, rounded to the nearest cent. Add this to the sale price to find the cost of the hockey stick: $57.85 + $3.47 = $61.32.
6. a.   This is a percent increase problem, so set up the proportion: change/original = percent/100. The change in attendance is 30 – 25 = 5. The original attendance is 25 members. The proportion setup is: . Cross multiply to get 25 × p = 5 × 100. Multiply 5 times 100 to get 25 × p = 500. Divide both sides by 25 to get p = 20. The percent increase is therefore 20%.
7. c.   The problem asks what percentage are NOT desserts. Because four of the 28 selections are desserts, then 28 – 4 = 24 selections are NOT desserts. Set up the proportion: part/whole = percent/100, and substitute the correct numbers: . Cross multiply: 28 × p = 24 × 100, or 28 × p = 2,400. Divide both sides by 28 to get the percent, rounded to the nearest tenth, of 85.7%.
8. a.   Twenty-five percent of the 1,032 voters voted for the incumbent. The key word of means multiply, and 25% is 0.25 written as a decimal. 0.25 × 1,032 = 258 voters.
9. e.   The tip is a percent increase to the price of the dinner, and 15% can be written as 0.15. 0.15 × 28 = 4.2. The tip is $4.20, which is added to the $28.00 to get $32.20.
10. b.   Set up an equation, changing 91% to a decimal, 0.91. The key word of means multiply and is means equals, so translate as 0.91 × n = 200.2. Divide 200.2 by 0.91 to get 220.

11. b.   Change the fraction to a decimal by long division, to get 0.9375. To change this decimal to a percent, move the decimal point two places to the right, to get 93.75%.
12. c.   To change a percent to a decimal, move the decimal point two places to the left: 23.5% = 0.235.
13. d.   To change 1.8 to a percent, move the decimal two places to the right. It is necessary to add a trailing zero as a placeholder: 1.8 = 180%.
14. a.   To solve this problem, remember that the key word of means multiply, and change the percent to a decimal: 12.8% = 0.128. Multiply 0.128 times 405 to get 51.84.
15. e.   Set up a proportion, using is/of = percent/100. The term immediately preceding the keyword is is 272, and the term following the keyword of is 400. The set up is: . Cross multiply to get 400 × p = 272 × 100. Multiply 272 times 100: 400 × p = 27,200. Divide both sides by 400 to get p = 68 or 68%.
16. d.   You can set up an equation, recalling that is means equals and of means multiply. For equations, the percent must also be converted to a decimal. A straight translation gives 533 = 0.82 × n. Divide both sides by 0.82 to get n = 650.
17. c.   Change 49% to a decimal to get 0.49. Since the key word of means multiply, multiply 0.49 times 3,000 to get 1,470.
18. e.   Set up a proportion. 4.25 is the part, since it precedes the key word is, and 25 is the whole, as it follows the key word of. Use is/of = percent/100. . Cross multiply to get 25 × p = 4.25 × 100. Multiply 4.25 times 100: 25 × p = 425. Divide both sides by 25 to get p = 17 or 17%.
19. d.   This is a percent increase problem, so set up a proportion: change/original = percent/100. The change is 1,350 – 1,200 = 150. The original number is 1,200. . Cross multiply to get 1,200 × p = 150 × 100. Multiply 150 times 100: 1,200 × p = 15,000. Divide both sides by 1,200 to get p = 12.5 or 12.5%.
20. a.   For percent decrease, set up a proportion: change/original = percent/100. The change is 25,670 – 24,500 = 1,170. The original population is 25,670. . Cross multiply to get 25,670 × p = 1,170 × 100. Multiply 1,170 by 100. 25,670 × p = 117,000. Divide both sides by 25,670 to get p = approximately 4.5578%, which rounds to the nearest tenth as 4.6%.