Question

Jayden and Carson are selling T-shirts and sweatshirts for a fundraiser. Jayden sells 9 T-shirts and 3 sweatshirts for $420. Carson sells 1 T-shirt and 6 sweatshirts for $296.

Write a system of equations (without solving it) representing the price of a T-shirt, t, and the price of a sweatshirt, s

Answer 1

9t + 3s = 420

t + 6s = 296

s =44; t = 32

Explanation:

Let

Price of a T-shirt = t

Price of a sweatshirt = s

Jayden:

9t + 3s = 420

Carson:

t + 6s = 296

9t + 3s = 420 (1)

t + 6s = 296 (2)

From (2)

t =296 - 6s

Substitute t =296 - 6s into (1)

9t + 3s = 420 (1)

9(296 - 6s) + 3s = 420

2664 - 54s + 3s = 420

2,664 - 51s = 420

-51s = 420 - 2,664

-51s = -2,244

s = 44

Substitute s = 44 into (2)

t + 6s = 296

t + 6(44) = 296

t + 264 = 296

t = 296 - 264

t = 32

s =44; t = 32