Question

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.

The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.

12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?

$5
$8
$12
$13

Answer 1

To solve for the cost of each jersey \( x \) and each pair of shorts \( y \), we can start with the given system of equations:

1. \( 12x + 12y = 156 \) (Equation 1)
2. \( 4x + 6y = 62 \) (Equation 2)

We can simplify Equation 1 by dividing everything by 12:

\[
x + y = 13 \quad (Equation 3)
\]

Now, let's simplify Equation 2 by dividing everything by 2:

\[
2x + 3y = 31 \quad (Equation 4)
\]

Now we have two simplified equations:

1. \( x + y = 13 \) (Equation 3)
2. \( 2x + 3y = 31 \) (Equation 4)

Next, we can solve Equation 3 for \( y \):

\[
y = 13 - x
\]

Now we can substitute this expression for \( y \) into Equation 4:

\[
2x + 3(13 - x) = 31
\]

Expanding this gives:

\[
2x + 39 - 3x = 31
\]

Combining like terms results in:

\[
-x + 39 = 31
\]

Subtracting 39 from both sides:

\[
-x = 31 - 39
\]

\[
-x = -8
\]

Multiplying both sides by -1 gives:

\[
x = 8
\]

Now that we've found \( x \) (the cost of each jersey), we can find \( y \) using Equation 3:

\[
y = 13 - x = 13 - 8 = 5
\]

Thus, the cost of each jersey is \( \boxed{8} \).