Question

Jacob and Jon bought some clothes from a sports shop. Jacob bought two T-Shirts and a pair of shorts. He spent $50. Jon bought one T-Shirt and one pair of shorts and spent $32.50. All the T-shirts were the same price. a. Form two simultaneous equations to show what they bought and spent. b. Solve your equations to find the cost of a T-shirt and a pair of shorts.

Answer 1

a.

2x + y = 50

x + y = 32.5

b.

T-shirt = $17.5

Pair of shorts = $15

Explanation:

a:

take x as the cost of a t-shirt and y as the cost of a pair of shorts.

Jacob = 2x + y = 50

Jon = x + y = 32.5

b:

Subtract equation 1 from equation 2

(2x + y = 50) - (x + y = 32.5)

This gives you

x + 0 = 17.5

so x = 17.5 = cost of 1 t-shirt

In order to find the value of y, substitute x into one of the equations and solve for y.

x + y = 32.5

17.5 + y = 32.5

y = 32.5 - 17.5

y = 15