CHAPTER_ppt_7_6 - 7.6 Proportions and Problem Solving with...

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Unformatted text preview: 7.6 Proportions and Problem Solving with Rational Equations Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Ratios and Rates A ratio is the quotient of two numbers or two quantities. The units associated with the ratio are important. The units should match. If the units do not match, it is called a rate , rather than a ratio. The ratio of the numbers a and b can also be written as a : b , or . b a Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 A proportion is two ratios (or rates) that are equal to each other. d c b a = We can rewrite the proportion by multiplying by the LCD, bd. This simplifies the proportion to ad = bc. This is commonly referred to as the cross product . Proportions Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Solve the proportion for x . 3 5 2 1 = + + x x ( 29 ( 29 2 5 1 3 + = + x x 10 5 3 3 + = + x x 7 2 =- x 2 7- = x Solving Proportions Continued. Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 3 5 2 3 2 5 =-- true Substitute the value for x into the original equation, to check the solution. So the solution is 2 7- = x 7 2 7 1 5 3 2 2 + = +-- Solving Proportions Example continued: Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 If a 170-pound person weighs approximately 65 pounds on Mars, how much does a 9000-pound satellite weigh? 170-pound person on Earth 65-pound person on Mars 9000-pound satellite on Earth-pound satellite on Mars x = 000 , 585 65 9000 170 = = x pounds 3441 170 / 585000 = x Solving Proportions Example: Martin-Gay, Beginning and Intermediate Algebra, 4ed 7 Given the following prices charged for various sizes of picante sauce, find the best buy....
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CHAPTER_ppt_7_6 - 7.6 Proportions and Problem Solving with...

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