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Published byShannon Walton Modified over 6 years ago

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EXAMPLE 4 Solve a multi-step problem CRAFTS You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform border as shown. You have enough chalkboard paint to cover 6 square feet. Find the width of the border to the nearest inch.

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EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Write a verbal model. Then write an equation. Let x be the width (in feet) of the border. 6 = (7 – 2x) (3 – 2x)

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EXAMPLE 4 Solve a multi-step problem STEP 2 Solve the equation. Write equation. 6 = (7 – 2x)(3 – 2x) Multiply binomials. 6 = 21 – 20x + 4x 2 Subtract 21 from each side. –15 = 4x 2 – 20x Divide each side by 4. – = x 2 – 5x 15 4 Add – 5 2, or 25 4, to each side. 2 25 4 – 15 4 + = x 2 – 5x + 25 4

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EXAMPLE 4 Solve a multi-step problem Write right side as the square of a binomial. – 15 4 + 25 4 = (x – ) 2 5 2 Simplify left side. 5 2 = (x – ) 5 2 2 Take square roots of each side. ± 5 2 = x – 5 2 Add 5 2 to each side. 5 2 ± 5 2 = x

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EXAMPLE 4 Solve a multi-step problem The solutions of the equation are and It is not possible for the width of the border to be 4.08 feet because the width of the door is 3 feet. So, the width of the border is 0.92 foot. Convert 0.92 foot to inches. 5 2 5 2 + 4.08 5 2 5 2 0.92 0.92 ft 12 in. 1 ft =11.04 in Multiply by conversion factor ANSWER The width of the border should be about 11 inches.

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GUIDED PRACTICE for Example 4 7. WHAT IF? In Example 4, suppose you have enough chalkboard paint to cover 4 square feet. Find the width of the border to the border to the nearest inch. ANSWER The width of the border should be about 13 inches.

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