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Example 3 A sports equipment store is having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccer ball bags for $155. Another soccer coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag. SOCCER Write and solve a linear system SOLUTION Write a system of equations. Let x represent the cost of a soccer ball, and let y represent the cost of a soccer ball bag. STEP 1

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Write and solve a linear system Example 3 Equation 1: Purchase by first soccer coach 10 x 2 y 155 += += Equation 2: Purchase by second soccer coach 12 x 3 y 189 += +=

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Write and solve a linear system Example 3 STEP 3 Subtract the equations. 6x 87= STEP 4 Solve for x. x 14.5= STEP 2 Multiply Equation 1 by 3 and Equation 2 by 2 so that the coefficient of y in each equation is the least common multiple of 3 and 2, or 6. 10x 2y = 12x 3y = 30x 6y = 24x 6y = 3 2

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Write and solve a linear system Example 3 STEP 5 Substitute 14.5 for x in either of the original equations and solve for y. Solve for y. y 5 = ANSWER A soccer ball costs $14.50, and a soccer ball bag costs $5. Write Equation 1. 10x 2y = Substitute 14.5 for x. 10 2y =()14.5

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Guided Practice 7.FABRIC Dina makes a quilt that has alternating stripes of quilting fabric and sateen fabric. Quilting fabric costs $4 per yard, and sateen fabric costs $6 per yard. She spends $76 on a total of 16 yards of the two fabrics. Find the amounts of quilting fabric and sateen fabric that Dina purchases. for Example 3 ANSWER 10 yd of quilting fabric and 6 yd of sateen

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