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?

Question

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 \[ \boxed{88} \]