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. Solve the system of equations for this situation.

Part A
Solve the system by ELIMINATION!! Show your work!

Answer 1

a T-shirt = $31

a sweatshirt = $44

Explanation:

Let T represent T-shirts and S represent sweatshirts.

Jayden sells 9 T-shirts and 3 sweatshirts for $420:

9T + 3S = 420

Carson sells 1 T-shirt and 6 sweatshirts for $296:

T + 6S = 296

• Multiply second equation with -9

-9T - 54S = -2,664

• Now find the the sum of two equation

9T - 9T + 3S - 54S = 420 - 2,664

-51S = -2,244

• Divide both sides by -51

S = 44 is the price for a sweatshirt, for the price of a T-shirt:

T + 6S = 296

• Rewrite equation by replacing S by 44

T + 6×44 = 296

T + 264 = 296

• Subtract 264 from boths sides

T = 31