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Step 3: Translate from English into an algebraic equation. We know that the area of the grass border is 320 ft2. We can calculate the area of the pond since we know its length and width. The pond plus grass border forms a large rectangle of length 20 2x and width 12 2x. The equation will come from the following relationship: Statement: Area of pond plus grass Area of pond Area of grass border Equation: (20 2x)(12 2x) 20(12) 320 Step 4: Solve the equation. (20 2x)(12 2x) 20(12) 320 240 64x 4x2 240 320 Multiply. 4x2 64x 320 Combine like terms. x2 16x 80 Divide by 4. x2 16x 80 0 Write in standard form. (x 20)(x 4) 0 Factor. x 20 0 or x 4 0 Set each factor equal to 0. x 20 or x 4 Solve. Step 5: Check the answer, and interpret the solution as it relates to the problem. x represents the width of the strip of grass, so x cannot equal 20. The width of the strip of grass is 4 ft. Check: Substitute x 4 into the equation written in Step 3. 20 2(4)12 2(4) 20(12) 320 (28)(20) 240 320 560 240 320 ✓ YOU TRY 4 A rectangular pond is 6 ft wide and 10 ft long and is surrounded by a concrete border of uniform width. The area of the border is 80 ft2. Find the width of the border. 4 Solve an Applied Problem Using a Quadratic Equation EXAMPLE 5 The total tourism-related output in the United States from 2000 to 2004 can be modeled by y 16.4x2 50.6x 896 where x is the number of years since 2000 and y is the total tourism-related output in billions of dollars. (www.bea.gov) a) According to the model, how much money was generated in 2002 due to tourism-related output? b) In what year was the total tourism-related output about $955 billion? www.mhhe.com/messersmith SECTION 10.4 Formulas and Applications 649


messersmith_power_intermediate_algebra_1e_ch4_7_10
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