LINEAR EQUATIONSAlgebraMultiplication of both sides of this equation by bd results in the following.(bd)^{a}bcd(bd)ad = cbThus, the product of the extremes of a proportion (ad) equals the product of the means (bc). Forexample, in the proportion 40 miles:80 miles = 1 hour:2 hours, the product of the extremes is (40miles)(2 hours) which equals 80 miles-hours, and the product of the means is (80 miles)(1 hour),which also equals 80 miles-hours.Ratio and proportion are familiar ideas. Many people use them without realizing it. When arecipe calls for 1½ cups of flour to make a serving for 6 people, and the cook wants to determinehow many cups of flour to use to make a serving for 8 people, she uses the concepts of ratiosand proportions. When the price of onions is 2 pounds for 49 cents and the cost of 3½ poundsis computed, ratio and proportion are used. Most people know how to solve ratio and proportionproblems such as these without knowing the specific steps used.Ratio and proportion problems are solved by using an unknown such as x for the missing term.The resulting proportion is solved for the value of x by setting the product of the extremes equalto the product of the means.Example 1:Solve the following proportion for x.Solution:5:x = 4:15The product of the extremes is (5)(15) = 75.The product of the means is (x)(4) = 4x.Equate these two products and solve the resulting equation.4x = 754x4754x18^{3}4MA-02 Page 14 Rev. 0

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