Percent Problems. Percent problems can be solved using proportions. Use the following formula when solving percent problems with a proportion.
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1 Percent Problems Percent problems can be solved using proportions. Use the following formula when solving percent problems with a proportion. The whole is the number after the word of. The percent is the number with the % sign. 100 The part is the remaining number which is being compared to the whole. Example 1 Find is 20% of 64. The percent is 20. The whole is the number after of, so the whole is 64. In this problem we don t know the part. Let represent the part. Fill the appropriate numbers in the percent proportion and solve for Write the cross products. Since x is multiplied by 100, divide each side of the equation by The original question was to find 20% of 64. Answer: 12.8 is 20% of 64. Example 2 Find is 5 % of 30. Page 1 of 7
2 The percent is 5. 5 can be written as the decimal The whole is the number after of, so the whole is 30. In this problem we don t know the part. Let represent the part. Fill the appropriate numbers in the percent proportion and solve for Write the cross products Since x is multiplied by 100, divide each side of the equation by The original question was to find 5 % of 30. Answer: is 5 % of 30. Example 3 Find is 150% of 20. The percent is 150. The whole is the number after of, so the whole is 20. In this problem we don t know the part. Let represent the part. Fill the appropriate numbers in the percent proportion and solve for Write the cross products Since x is multiplied by 100, divide each side of the equation by Page 2 of 7
3 The original question was to find 150% of 20. Answer: 30 is 150% of 20. Example 4 Find is 4 % of 30. When solving this problem change the fraction to a decimal. The percent is 4. 4 can be written as the decimal Carry the repeating decimal out several places so you will have an accurate answer. The whole is the number after of, so the whole is 30. In this problem we don t know the part. Let represent the part. Fill the appropriate numbers in the percent proportion and solve for Write the cross products Since x is multiplied by 100, divide each side of the equation by The original question was to find 4 % of 30. Answer: 1.3 is 4 % of 30. Example 5 Find is 4 % of 30. This problem can also be solved by keeping 4 as a fraction instead of making it a decimal. Page 3 of 7
4 Write the cross products Change 4 to an improper fraction Since x is multiplied by 100, divide each side of the equation by Answer: 1.3 You get the same answer as before in example 4. Example 6 20 is what % of 80? The percent is unknown since the question is what percent. Let represent the percent. The whole is the number after of, so the whole is 80. The part is the remaining number Write the cross products Since x is multiplied by 80, divide each side of the equation by The original question was 20 is what % of 80? Page 4 of 7
5 Since the question was what percent, there will be a percent sign in the answer. Answer: 25% Example 7 25 is what % of 20? The percent is unknown since the question is what percent. Let represent the percent. The whole is the number after of, so the whole is 20. The part is the remaining number Write the cross products Since x is multiplied by 20, divide each side of the equation by The original question was 25 is what % of 20? Since the question was what percent, there will be a percent sign in the answer. Answer: 125% Example 8 15% of what number is 40? The percent is 15. The whole is the number after of. The whole is unknown since the question is of what number. Let represent the whole. Page 5 of 7
6 The part is the remaining number Write the cross products Since x is multiplied by 15, divide each side of the equation by Since.6 = the answer can also be written as 266. The original question was 15% of what number is 40? Answer: 15% of is 40. Example % of what number is 30? Round the answer to the nearest hundredths. The percent is The whole is the number after of. The whole is unknown since the question is of what number. Let represent the whole. The part is the remaining number Write the cross products. Page 6 of 7
7 Since x is multiplied by 5.25, divide each side of the equation by = = Rounded to the nearest hundredth. The original question was 5.25% of what number is 30? Answer: 5.25% of is 30. Brenda Moore and Indian Hills Community College Page 7 of 7
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