7.2 Translating and Solving Percent Problems


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1 7.2 ranslating and Solving Percent Problems In this section we will study how to solve percent problems. Percent problems usually have a phrase in the question in one of the following forms: Percent of Whole is Part Part is Percent of Whole We will solve these types of problems by translating these questions into an algebraic equation as we did in Section 5.7. We will look for key words and use them to create an equation which we solve. he two most important key words for this section are is and of: is means equal (=), and of means multiply (). Also, the word what is an indicator of an unknown quantity, which we will represent with a variable. hen, we will use solving methods that we first examined in Chapter 5. PARS OF A PERCEN PROBLEM PERCEN WHOLE PAR Rate or portion of 00 he total amount he portion of the whole he % symbol follows the number P will be used as the variable for Percent Follows the word of W will be used as the variable for Whole Will be found on the other side of the word is will be used as the variable for Par Note: When solving percent problems algebraically, you will need to change the percent to its decimal form. Recall from the last section that you change a percent to a decimal by dividing by 00. If the percent is the missing element from the problem, the algebraic answer to the equation that is solved will be in decimal form. hus, you will need to change the decimal form into a percent in your final answer. Recall from the last section that you change a decimal to a percent by multiplying by 00%. In the next few examples, the unknown value will be the percent. When we solve the equation, the value will be given as a decimal and we will need to change it to a percent for our final answer. 478
2 Example : What percent of 20 is 5? We need to determine the Percent. Use P to represent the percent. Statement: What percent of 20 is 5? Equation: P 20 = 5 Next, solve this equation for P. P20 5 P P 0.25 P % 25% Divide both sides by 20. his is the decimal form. Change to a percent by multiplying by 00%. Practice : What percent of 72 is 36? Answer: 50% Example 2: What percent of 320 is 64? We need to determine the Percent. Use P to represent the percent. Statement: What percent of 320 is 64? Equation: P 320 = 64 Next, solve this equation for P. P P P 0.2 P % 20% Divide both sides by 320. his is the decimal form. Change to a percent by multiplying by 00%. Practice 2: What percent of 200 is 50? Answer: 25% 479
3 Example 3: 20 is what percent of 80? We need to determine the Percent. Use P to represent the percent. Statement: 20 is what percent of 80 Equation: 20 = P 80 Next, solve this equation for P. 20 P80 20 P P P.500% 50% Divide both sides by 80. his is the decimal form. Change to a percent by multiplying by 00%. Practice 3: 42 is what percent of 68? Answer: 25% Example 4: What percent of 96 is 80? We need to find the Percent. Use P to represent the percent. Statement: What percent of 96 is 80? Equation: P 96 = 80 Next, solve this equation for P. P96 80 P96 80 Divide both sides by he decimal form of this fraction gives a repeating decimal. herefore, we simplify this fraction and then change the fraction into a percent P Factor the numerator and denominator P Divide out common factors % P Change to a percent by multiplying by 00% P % Simplify by dividing out common factors P 83 % his is the percent as a mixed number
4 Practice 4: What percent of 20 is 90? Answer: 75% In the next few problems the unknown value will be the part. We must remember to change the percent value that is given to a decimal before we solve the equation. Example 5: 8% of 220 is what number? We need to determine the Par. Use to represent the part. Statement: 8% of 220 is what? Equation: = Next, solve this equation for Multiply to solve. Practice 5: 5% of 60 is what number? Answer: 9 Example 6: What is 20% of 35? We need to determine the Par. Use to represent the part. Statement: What is 20% of 35? Equation: = Next, solve this equation for Multiply to solve. Practice 6: What is 30% of 90? Answer:
5 Example 7: What is 300% of 7? We need to determine the Par. Use to represent the part. Statement: What is 300% of 7? Equation: = 3 7 Next, solve this equation for Multiply to solve. Practice 7: What is 45% of 60? Answer: 87 Example 8: What is 5 % 2 of 248? When given the percent we must convert it to a decimal. 5 % % We need to determine the Par. Use to represent the part. Statement: What is 5 % 2 of 248? Equation: = Next, solve this equation for Multiply to solve. Practice 8: What is 3 % 5 of 325? Answer: In the next few problems the unknown value will be the whole. We must remember to change the percent value that is given to a decimal before we solve the equation. 482
6 Example 9: 30 is 5% of what? We need to determine the Whole. Use W to represent the whole. Statement: 30 is 5% of What? Equation: 30 = 0.5 W Next, solve this equation for W W W W Divide both sides by 0.5. Practice 9: 60 is 5% of what number? Answer: Example 0: 80% of what number is 8? We need to determine the Whole. Use W to represent the whole. Statement: 80% of what is 8 Equation:.8 W = 8 Next, solve this equation for W..8W 8.8W W 45 Divide both sides by.8. Practice 0: 200% of what number is 90? Answer:
7 Example : 45 is 30% of what? We need to determine the Whole. Use W to represent the whole. Statement: 45 is 30% of What? Equation: 45 = 0.3 W Next, solve this equation for W W W W Divide both sides by 0.3. Practice : 32 is 20% of what number? Answer: 60 We can also solve percent problems as we did proportion ratio problems in Chapter 6. With this method you will not need to convert percents to decimals or decimals to percents. Every problem is set up the same no matter what the unknown value is. SOLVING PERCEN PROBLEMS USING PROPORIONS Percent 00 Part Whole Example 2: What percent of 20 is 5? We need to determine the Percent. Whole = 20 Part = 5 Fill in the proportion with the known information and solve for the unknown. P P 500 Cross multiply. 20P P 25% Divide. he answer is in percent form. Practice 2: What percent of 72 is 36? Answer: 50% 484
8 Example 3: What is 8% of 220? We need to determine the Par. Whole = 220 Percent = 8 Fill in the proportion with the known information and solve for the unknown Cross multiply. Divide. Practice 3: 5% of 60 is what number? Answer: 9 Example 4: 30 is 5% of what? We need to determine the Whole. Part = 30 Percent = 5% Fill in the proportion with the known information and solve for the unknown W 5W W W 200 Cross multiply. Divide. Practice 4: 60 is 5% of what number? Answer: Watch All: 485
9 7.2 ranslating and Solving Percent Problems Exercises. What is 30% of 300? 2. What is 8.9% of 0? 3. 20% of 4000 is what? 4. 5% of 90 is what? is 25% of what? is 80% of what? 7. What percent of 25 is 25? 8. What percent of 00 is 50? is what percent of 400? is what percent of 60?. What is 25% of 225? 2. What is 68% of 80? 3. What is 33 % of 25? 4. 25% of 200 is what? % of 86.5 is what? 6. 5 is 25% of what? is 80% of what? is 20% of what? is % of what? is.5% of what? 2. 0 is what percent of 50? is what percent of 00? is what percent of 260? is what percent of 20? is what percent of 20,000? 486
10 7.2 ranslating and Solving Percent Problems Exercise Answers % 8. 50% 9. 0% 0. 40% or or or , , % 22. 2% % % or 2 % 25..0% or % 487
11 CCBC Math 08 Sections7. to 7.2 CHAPER 7 MidChapter Review. Convert to a fraction: 25% 2. Convert to a fraction: 93% 3. Convert to a fraction: 4. Convert to a percent: 5. Convert to a percent: % Convert to a percent: Convert to a percent: Convert to a decimal: 5.9% 9. Convert to a decimal: 8.5% 0. Convert to a decimal: 6%. What percent of 300 is 90? 2. What percent of 62 is 58.9? 3. What is 25% of 200? 4. What is 8% of 420? is 20% of what? is 88% of what? 7. What percent of 45 is 9? 8. 99% of 90 is what? is what percent of 425? is what percent of 60? 2. 47% of 70 is what number? 22. What is 25% of 60? % of what number is 550? 24. What is 83 % 3 of 96? 25. What percent of 320 is 64? 26. What percent of 200 is 230? 27. What percent of 20 is 2? % of what number is 642? % of what number is 96? 30. What is 82% of 00?
12 CCBC Math 08 MidChapter 7 Review Sections 7. to 7.2 M i d  C h a p t e r 7 R e v i e w A n s w e r s % % % % % 2. 95% % % % % 26. 5% %
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