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### Chapter 6 - Percent

Course: MTH 090, Spring 2009
School: Moraine Valley...
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Word Count: 812

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6 Percent Chapter Chapter Sections 6.1 Percents, Decimals, and Fractions 6.2 Solving Percent Problems Using Equations 6.3 Solving Percent Problems Using Proportions 6.4 Applications of Percents 6.5 Percent and Problem Solving: Sales Tax and Commissio 6.6 Percent and Problem Solving: Interest Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 2 6.1 Percents, Decimals, and Fractions...

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6 Percent Chapter Chapter Sections 6.1 Percents, Decimals, and Fractions 6.2 Solving Percent Problems Using Equations 6.3 Solving Percent Problems Using Proportions 6.4 Applications of Percents 6.5 Percent and Problem Solving: Sales Tax and Commissio 6.6 Percent and Problem Solving: Interest Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 2 6.1 Percents, Decimals, and Fractions Understanding Percent Step Example Percent: Means per one hundred, the % symbol is used to denote percent. 48 of 100 squares are shaded or 48% is shaded. 48 = 48 % 100 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 4 Writing Percent as Decimals EXAMPLE 67% of American men are happy with their current weight. Convert this percentage into a decimal. (Source: Gallup for Wheat Foods Council) SOLUTION Replace the % symbol with its decimal equivalent. 67% 67(0.01) 67(0.01) = .67 .67 of American men are happy with their current weight. Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 5 Writing Decimals as Percents EXAMPLE The Munoz family saves 0.10 of their take-home pay. Convert this decimal to a percent. SOLUTION Multiply the decimal by 1 in the form of 100%. 0.10 0.10(100%) 0.10(100%) = 10.% or 10% The Munoz family saves 10% of their take-home pay. Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 6 Writing Percents as Fractions EXAMPLE Write 4.5% as a fraction or mixed number in simplest form. SOLUTION Replace the percent symbol with its fraction equivalent. 4 .5 % 1 4.5 100 1 4.5 100 4.5 10 = 100 10 Multiply by 1 in 10 the form of to 10 remove the decimal in the numerator. 45 9 = = 1000 200 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 7 Writing Fractions as Percents EXAMPLE 2 5 Write as a percent. SOLUTION 2 5 Multiply the fraction by 1 in the form of 100% 2 100% 5 1 200% = 40% = 5 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 8 Converting Percents, Decimals, and Fractions EXAMPLE Complete the following table. SOLUTION Percent Decimal 50% 0.5 40% 0. 4 25% 0.25 12.5% 0.125 62.5% 0.625 14% 0.14 Fraction 1 2 2 5 1 4 1 8 5 8 7 50 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 9 6.2 Solving Percent Problems Using Equations Writing Percent Problems as Equations EXAMPLE 72% of 63 is what number? SOLUTION of means multiplication () is means equals (=) what (or some equivalent) means the unknown number 72% of 63 is what number? 72% 63 = n Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 11 Solving Percent Problems Formula percent base = amount Example 25% of 60 is what number? percent base amount 0.25 60 = n n = 15 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 12 6.3 Solving Percent Problems Using Proportions Writing Percent Problems as Proportions Formula Example 92% of 30 is what number? amount percent = base 100 percent base amount n 92 = 30 100 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 14 Solving Percent Problems EXAMPLE 25% of 84 is what number? SOLUTION n 25 = 84 100 n 84 = 1 4 n 4 = 84 1 84 n= 4 n = 21 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 15 6.4 Applications Applications of Percents Solving Involving Percent EXAMPLE 18% of Franks wages are withheld for income tax. Find the amount withheld from Franks wages of \$3680 per month. SOLUTION Amount = n Base = \$3680 Percent = 18% n = 0.18 3680 3680 = 0.18 29440 3680 62240 \$662.40 is the amount withheld from Franks wages. Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 17 Finding Percent Increase and Percent Decrease Formula percent of increase = amount of increase original amount EXAMPLE The average soft-drink size has increased from 13.1 oz to 19.9 oz over the past two decades. Find the percent increase. (Source: University of North Carolina at Chapel Hill, Journal for American Medicine) SOLUTION 19.9 - 13.1 13.1 6.8 10 68 = = 13.1 10 131 percent of increase = = 51.9% Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 18 Finding Percent Increase and Percent Decrease Formula percent of decrease = amount of decrease original amount EXAMPLE John Smith decided to decrease the number of calories in his diet from 3250 to 2100. Find the percent decrease. SOLUTION 3250 - 2100 3250 23 1150 = = 3250 65 percent of decrease = = 0.354 = 35.4% Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 19 6.5 Percent and Problem Solving: Sales Tax and Commission Calculating Sales Tax and Total Price Formulas sales tax = tax rate purchase price total price = purchase price + sales tax EXAMPLE A gold and diamond bracelet sells for \$1800. Find the total price if the sales tax rate is 6.5%. SOLUTION sales tax = .065 1800 = \$117 total price = 1800 + 117 = \$1917 The total price of the gold and diamond bracelet is \$1917. Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 21 Calculating Commissions Definition Wage: Payment for performing work. Example A salesperson earned a commission of \$3575 for selling \$32,500 worth of books to various bookstores. Find the commission rate. Commission: Pay for a SOLUTION percentage of an commission employees total sales. commission rate = = commission rate sales commission 3575 = sales 32,500 = 0.11 = 11% Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 22 Calculating Discount and Sale Price Formulas amount of discount = discount rate original price sale price = original price - amount of discount EXAMPLE A \$2000 designer dress is on sale for 30% off. Find the discount and the sale price. SOLUTION discount = 0.30 2000 = \$600 total price = 2000 - 600 = \$1400 The price of the designer dress after a \$600 rebate is \$1400. Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 23 6.6 Percent and Problem Solving: Interest Calculating Simple Interest Definition Interest: Money charged for using other peoples money. Principal amount or Principal: Money borrowed, loaned, or invested. Interest Rate: The percent used in computing the interest. Simple Interest: Interest computed on the original principal. Example A company borrows \$62,500 for 2 years at a simple interest of 12.5% to buy an airplane. Find the total amount paid on the loan. SOLUTION simple interest = principal rate time = 62,500 0.125 2 = 15,625 total amount = principal + interest = 62,500 + 15,625 = \$78,125 Martin-Gay, Martin-Gay, Basic College Mathematics with Early Integers 25
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