Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $\$131$ on $9$ new shirts and $4$ pairs of shorts. The older brother purchased $9$ new shirts and $5$ pairs of shorts and paid a total of $\$148$ . How much did each item cost? $\newline$ Each shirt cost $\$\_\_\_\_$ , and each pair of shorts cost $\$\_\_\_\_$ .

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent

\$131

9

new shirts and

4

pairs of shorts. The older brother purchased

9

new shirts and

5

pairs of shorts and paid a total of

\$148

. How much did each item cost?

\newline

Each shirt cost

\$\_\_\_\_

, and each pair of shorts cost

\$\_\_\_\_

Define Prices: Let's denote the price of each shirt as $s$ and the price of each pair of shorts as $p$ . The younger brother spent $\$131$ on $9$ shirts and $4$ pairs of shorts, which gives us the equation $9s + 4p = 131$ .
Younger Brother's Purchase: The older brother purchased $9$ shirts and $5$ pairs of shorts for a total of $\$148$ , which gives us the equation $9s + 5p = 148$ .
Elimination Method: We now have a system of two equations. To use elimination, we need to eliminate one of the variables, $s$ or $p$ . Since the coefficients of $s$ are the same in both equations, we can eliminate $s$ by subtracting the first equation from the second.
Calculate Shorts Price: Subtracting the first equation from the second, we get $9s + 5p - (9s + 4p) = 148 - 131$ , which simplifies to $p = 17$ .
Substitute and Solve: Now that we have the value of $p$ , we can substitute it back into the first equation to find the value of $s$ . Substituting $p = 17$ into the first equation, we get $9s + 4(17) = 131$ .
Calculate Shirt Price: Solving for $s$ , we have $9s + 68 = 131$ . Subtracting $68$ from both sides, we get $9s = 63$ .
Final Prices: Dividing both sides by $9$ , we find that $s = 7$ . So, each shirt costs $\$7$ .
Final Prices: Dividing both sides by $9$ , we find that $s = 7$ . So, each shirt costs $\$7$ .We have found that each shirt costs $\$7$ and each pair of shorts costs $\$17$ .