6.3 Applications of Algebra 317 Cross-Multiplication If a b c d , = then = ≠ ≠ ad bc b d , where 0, 0. Let’s use cross-multiplication to solve the proportion x x 2 5 5 8 . + = + + = + + = + + = + + = = = x x x x x x x x x 2 5 5 8 8( 2) 5( 5) 8 16 5 25 3 16 25 3 9 3 Cross-multiplication Notice we obtained the same answer as we did by multiplying both sides of the equation by the LCD, 40. Many practical application problems can be solved using proportions. SOLVING APPLICATION PROBLEMS USING PROPORTIONS 1. Represent the unknown quantity by a variable. 2. Set up the proportion by listing the given ratio on the left-hand side of the equation and the unknown quantity and other given quantity on the right-hand side of the equation. When setting up the right-hand side of the proportion, the same respective quantities should occupy the same respective positions on the left and right. For example, an acceptable proportion might be miles hour miles hour = 3. Once the proportion is properly written, use cross multiplication to solve the equation. 4. Answer the question or questions asked using the appropriate units. PROCEDURE Example 5 Water Usage The cost for water in Tulsa, Oklahoma, is $4.31 per 1000 gallons (gal) of water used. a) The Chens live in Tulsa, and during September they used 12,451 gallons of water. What was the Chens’ cost for water? b) During October, the Chens’ cost for water was $49.73. How many gallons of water did they use? Solution a) The unknown quantity in this problem is the cost for 12,451 gallons of water. We let x cost for 12,451 gallons of water. = Then, we set up a proportion to solve this problem. The proportion we use is = = ⎧ ⎨ ⎩ x costof 1000gal 1000 gal cost of 12,451 gal 12,451 gal 4.31 1000 12,451 Given ration m Tulsa, Oklahoma Sepavo/123RF
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