EXAMPLE 3
Standardized Test Practice
SOLUTION
Write verbal models for this situation.
EXAMPLE 3
Equation 1
Equation 2
Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
STEP 2 Write a system of equations.
Equation 1 5x + 7y = 2500 Total cost for all T-shirts
Equation 2 8x + 12y = 4200 Total revenue from all T-shirts sold
STEP 3 Solve the system using the elimination method.
Multiply Equation 1 by – 8 and Equation 2 by 5 so that
the coefficients of x differ only in sign.
5x + 7y = 2500
– 40x – 56y = – 20,000
40x + 60y = 21,000
8x + 12y = 4200
Add the revised equations and solve for y. 4y = 1000
y = 250
EXAMPLE 3
Standardized Test Practice
Substitute the value of y into one of the original
equations and solve for x.
5x + 7y = 2500
5x + 7(250) = 2500
5x + 1750 = 2500
x = 150
Write Equation 1.
Substitute 250 for y.
Simplify.
Solve for x.
The school sold 150 short sleeve T-shirts and 250
long sleeve T-shirts.
ANSWER
The correct answer is C.
GUIDED PRACTICE
for Example 3
4.
WHAT IF? In Example 3, suppose the school spends a
total of $3715 on T-shirts and sells all of them for
$6160. How many of each type of T-shirt are sold?
STEP 1 Write verbal models for this situation.
Equation 1
5
x
+
7
y
= 3715
GUIDED PRACTICE
for Example 3
Equation 2
8
x
+
12
y
= 6160
STEP 2 Write a system of equations.
Equation 1 5x + 7y = 3715 Total cost for all T-shirts
Equation 2 8x + 12y = 6160 Total revenue from all T-shirts sold
GUIDED PRACTICE
for Example 3
STEP 3 Solve the system using the elimination method.
Multiply Equation 1 by – 8 and Equation 2 by 5 so that
the coefficients of x differ only in sign.
5x + 7y = 3715
– 40x – 56y = – 29720
40x + 60y = 30800
8x + 12y = 6160
Add the revised equations and solve for y. 4y = 1080
y = 270
GUIDED PRACTICE
for Example 3
Substitute the value of y into one of the original
equations and solve for x.
5x + 7y = 3715
5x + 7(270) = 3715
5x + 1890 = 3715
x = 365
Write Equation 1.
Substitute 250 for y.
Simplify.
Solve for x.
ANSWER
The school sold 365 short sleeve T-shirts and 270
long sleeve T-shirts.