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 representthe cost of a soccer ball, and let y representthe cost of a soccer ball bag.

STEP 1

Write and solve a linear systemExample 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

• + =•

• + =•

Write and solve a linear systemExample 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 155+ =

12x 3y 189+ =

30x 6y 465+ =

24x 6y 378+ =

3

2

Write and solve a linear systemExample 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 155+ =

Substitute 14.5 for x.10 2y 155+ =( )14.5

Guided Practice

7. FABRICDina 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