Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 2.4 Formulas and Percents Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

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3 Solving a Formula for a Variable We know that solving an equation is the process of finding the number or numbers that make the equation a true statement. Formulas contain two or more letters, representing two or more variables. The formula for the perimeter P of a rectangle is P = 2l + 2w where l is the length and w is the width of the rectangle. We say that the formula is solved for P, since P is alone on one side and the other side does not contain a P.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 Solving a Formula for a Variable Solving a formula for a variable means using the addition and multiplication properties of equality to rewrite the formula so that the variable is isolated on one side of the equation. To solve a formula for one of its variables, treat that variable as if it were the only variable in the equation. Think of the other variables as if they were just numbers. Use the addition property of equality to isolate all terms with the specified variable on one side. Then use the multiplication property of equality to get the specified variable alone. The next example shows how to do this.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 The area, A, of a rectangle with length l and width w is given by the formula A = lw. l w l Area of a Rectangle

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 The perimeter, P, of a rectangle with length l and width w is given by the formula P = 2l + 2w. l w Perimeter of a Rectangle

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Solve the perimeter equation for w. 2w + 2l = P 2w + 2l – 2l = P – 2l Subtract 2l from both sides. 2w = P – 2l Simplify. Divide both sides by 2. Simplify. Solving a Formula for a Variable

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8 Solve the perimeter equation for w. 2w + 2l = P 2w + 2l – 2l = P – 2l Subtract 2l from both sides. 2w = P – 2l Simplify. Divide both sides by 2. Simplify. Solving a Formula for a Variable

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 9 Solving a Formula for a VariableEXAMPLE SOLUTION Solve the formula y = mx + b for x. y = mx + b y – b = mx + b – b Subtract b from both sides. y – b = mx Simplify. Divide both sides by m to find x.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Solving a Formula for a VariableEXAMPLE SOLUTION Solve the formula y = mx + b for x. y = mx + b y – b = mx + b – b Subtract b from both sides. y – b = mx Simplify. Divide both sides by m to find x.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Objective #1: Examples

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Percents are the result of expressing numbers as a part of 100. The word percent means per hundred or 1/100. If 45 of every 100 students take Introductory Algebra, then 45% of the students take Introductory Algebra. As a fraction, it is written Percents

Copyright © 2013, 2009, 2006 Pearson Education, Inc Move the decimal point two places to the right. 2.Attach a percent sign. Writing Decimals as Percents Using the definition of percent, you should be able to write decimals as percents and also be able to write percents as decimals. Here is the rule for writing a decimal as a percent.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Express 0.47 as a percent = 47% (since percent means 1/100, both sides here mean “47/100.”) Express 1.25 as a percent = 125% When we insert a percent sign, we move the decimal point two places to the right. Writing Decimals as PercentsEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Use the following steps to write a percent as a decimal. 1.Move the decimal point two places to the left. 2.Remove the percent sign. Writing Percents as Decimals

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Express 63% as a decimal. 63% = 0.63 Express 150% as a decimal. 150% = 1.50 Writing Percents as DecimalsEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 A = P · B In the formula, A = PB B = Base Number P = Percent written as a decimal A = The number compared to B A isP percentofB Percent Formula

Copyright © 2013, 2009, 2006 Pearson Education, Inc is what percent of 12? 8 = P · 12 8isP percentof12 Using the Percent FormulaEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc is what percent of 12? 8 = P · 12 8isP percentof12 Using the Percent FormulaEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 What is 12% of 8? A = 0.12 · 8 A = 0.12(8) A = 0.96 Thus, 12% of 8 is Whatis12 percent of8 Using the Percent FormulaEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 What is 12% of 8? A = 0.12 · 8 A = 0.12(8) A = 0.96 Thus, 12% of 8 is Whatis12 percent of8 Using the Percent FormulaEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc is 25% of what number? 5 = 0.25 · B 5 = 0.25B 5is25 percentofwhat number? Using the Percent FormulaEXAMPLE

Copyright © 2013, 2009, 2006 Pearson Education, Inc is 25% of what number? 5 = 0.25 · B 5 = 0.25B 5is25 percentofwhat number? Using the Percent FormulaEXAMPLE

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 39 Percent Increase and Decrease Percents are used for comparing changes, such as increases or decreases in sales, population, prices, and production. If a quantity changes, its percent increase or percent decrease can be determined by asking the following question: The change is what percent of the original amount? The question is answered using the percent formula as follows: Percent Increase Percent Decrease The is what of the original The is what of the original increase percent amount decrease percent amount

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 40 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 40 Objective #3: Examples

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