Question

you and your friend go to a store where all the shirts cost the same amount and all the pants cost same amount.

• you buy 1 shirt and 3 pairs of pants for $35.
• your friend buys 3 shirts and 2 pairs of pants for $42.

what is the cost for each shirt and each pair of pants?
each shirt costs $
each pair of pants costs $

Explanation:

Step1: Define variables

Let \( s \) be the cost of one shirt (in dollars) and \( p \) be the cost of one pair of pants (in dollars).

Step2: Set up equations

From the problem, we have two equations:

1. You buy 1 shirt and 3 pairs of pants for $35: \( s + 3p = 35 \)
2. Your friend buys 3 shirts and 2 pairs of pants for $42: \( 3s + 2p = 42 \)

Step3: Solve the first equation for \( s \)

From \( s + 3p = 35 \), we can express \( s \) as \( s = 35 - 3p \).

Step4: Substitute \( s \) into the second equation

Substitute \( s = 35 - 3p \) into \( 3s + 2p = 42 \):
\[

$$\begin{align*} 3(35 - 3p) + 2p &= 42 \\ 105 - 9p + 2p &= 42 \\ 105 - 7p &= 42 \\ -7p &= 42 - 105 \\ -7p &= -63 \\ p &= \frac{-63}{-7} \\ p &= 9 \end{align*}$$

\]

Step5: Find \( s \) using \( p = 9 \)

Substitute \( p = 9 \) into \( s = 35 - 3p \):
\[
s = 35 - 3(9) = 35 - 27 = 8
\]

Answer:

Each shirt costs $\boldsymbol{8}$
Each pair of pants costs $\boldsymbol{9}$