Question

(HELP ASAP PLEASE!!)

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 $79 on 4 new shirts and 3 pairs of shorts. The older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185. How much did each item cost?


Each shirt cost $ ___ and each pair of shorts cost $ ___ .

Answer 1

Each shirt cost $7 and each pair of shorts cost $17 .

Explanation:

let shirts be represented as x

let shorts be represented as y

Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.

4 x + 3 y = $79 .......equation 1

Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.

7 x + 8 y = $185 .......equation 2

multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.

7 × (4 x + 3 y = $79) ⇒ +28 x + 21 y = $553

-4 × (7 x + 8 y = $185) ⇒ -28 x - 32 y = - $740

0 - 11 y = - $187 ⇒ -11 y = - $187

y =
`(- $187)/(- 11)` ⇒ y = $17

shorts = y = $17

put value of y in equation 1

4 x + 3 ( $17 ) = $79 ⇒ 4x + $51 = $79 ⇒ 4x = $79 - $51

4x = $28 ⇒ x =
`($28)/(4)` ⇒ x = $7

Shirts = x = $7