(asap ) 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 $ .

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

Step-by-step 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 =   ⇒   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 =   ⇒   x = $7

Shirts = x = $7

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