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Example 3
Write and solve a linear system
SOCCER
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.
SOLUTION
STEP 1 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.
Example 3
Write and solve a linear system
Equation 1: Purchase by first soccer coach
•
10
•
•
+
x
+
2
•
=
y
=
155
Equation 2: Purchase by second soccer coach
•
12
•
•
+
x
+
3
•
=
y
=
189
Example 3
Write and solve a linear system
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
3
30x + 6y = 465
12x + 3y = 189
2
24x + 6y = 378
STEP 3 Subtract the equations.
STEP 4 Solve for x.
6x
= 87
x = 14.5
Example 3
Write and solve a linear system
STEP 5 Substitute 14.5 for x in either of the original
equations and solve for y.
10x + 2y = 155
10 (14.5) + 2y = 155
y = 5
Write Equation 1.
Substitute 14.5 for x.
Solve for y.
ANSWER
A soccer ball costs $14.50, and a soccer ball bag costs $5.
Guided Practice
for Example 3
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.
ANSWER
10 yd of quilting fabric and 6 yd of sateen