Question

the manager of a clothing chain buys pants from a distributor. the manager purchased 35 pairs of pants and 25 pairs of shorts for one of his stores. the cost was $650. the manager purchased 55 pairs of pants and 35 pairs of shorts for another store. the cost was $1,000. the price for each pair of pants is $ choose and for each pair of shorts is $ choose. which numbers makes each statement true? click or tap the correct number from each drop - down menu.

Explanation:

Step1: Define variables

Let $p$ = price of pants, $s$ = price of shorts.

Step2: Set up system of equations

$$35p + 25s = 650$$
$$55p + 35s = 1000$$

Step3: Simplify first equation

Divide by 5: $7p + 5s = 130$

Step4: Simplify second equation

Divide by 5: $11p + 7s = 200$

Step5: Eliminate $s$ (multiply equations)

Multiply Step3 by 7: $49p + 35s = 910$
Multiply Step4 by 5: $55p + 35s = 1000$

Step6: Subtract equations

$(55p + 35s) - (49p + 35s) = 1000 - 910$
$6p = 90$

Step7: Solve for $p$

$p = \frac{90}{6} = 15$

Step8: Solve for $s$ (substitute $p$)

$7(15) + 5s = 130$
$105 + 5s = 130$
$5s = 25$
$s = 5$

Answer:

The price for each pair of pants is $\$15$ and for each pair of shorts is $\$5$.