Question

A clothing company sells slacks that are either blue or gray and pleated or non-pleated. Last month, the company sold 5 times as many pairs of blue pleated slacks as gray pleated slacks, and it sold twice as many pairs of gray non-pleated slacks as blue non-pleated slacks. If it sold 333 pairs of blue slacks and 225 pairs of gray slacks, how many pairs of blue non-pleated slacks did it sell?
49
88
176
245

Answer 1

Let:
- \( x \) be the number of gray pleated slacks sold.
- \( 5x \) be the number of blue pleated slacks sold (since it is 5 times the number of gray pleated slacks).
- \( y \) be the number of blue non-pleated slacks sold.
- \( 2y \) be the number of gray non-pleated slacks sold (since it is twice the number of blue non-pleated slacks).

From the problem, we know:
1. The total number of blue slacks sold is:
\[
5x + y = 333
\]

2. The total number of gray slacks sold is:
\[
x + 2y = 225
\]

Now we can solve these two equations step by step.

First, we can express \( y \) in terms of \( x \) from the first equation:
\[
y = 333 - 5x
\]

Next, substitute \( y \) in the second equation:
\[
x + 2(333 - 5x) = 225
\]
Simplifying this expression:
\[
x + 666 - 10x = 225
\]
Combine like terms:
\[
666 - 9x = 225
\]
Now, isolate \( 9x \):
\[
666 - 225 = 9x
\]
\[
441 = 9x
\]
Now, divide both sides by 9:
\[
x = \frac{441}{9} = 49
\]

Now that we have \( x \) (the number of gray pleated slacks), we can find \( y \) using the first equation:
\[
y = 333 - 5(49)
\]
\[
y = 333 - 245 = 88
\]

Now, we have:
- Gray pleated slacks: \( x = 49 \)
- Blue pleated slacks: \( 5x = 5 \times 49 = 245 \)
- Blue non-pleated slacks: \( y = 88 \)
- Gray non-pleated slacks: \( 2y = 2 \times 88 = 176 \)

Therefore, the number of pairs of blue non-pleated slacks sold is
\[
\boxed{88}
\]