Question

Matt paid $5.30 for 3 bags of chips and 2 sodas. Rob spent $7.50 on 4 bags of chips and 3 sodas.

a. Type your system of equations.

b. How much is each bag of chips and each soda?

Answer 1

bag of chips is $0.90

soda is $1.30

Explanation:

let C is the price of bag of chips and S is the price of the soda

Matt paid $5.30 for 3 bags of chips and 2 sodas

3C + 2S = 5.30 equation 1

Rob spent $7.50 on 4 bags of chips and 3 sodas.

4C + 3S = 7.50 equation 2

multiply eq.1 by -3 and eq.2 by 2

-3(3C + 2S = 5.30)

-9C - 6S = -15.90 equation 3

2(4C + 3S = 7.50)

8C + 6S = 15 equation 4

add eq.3 and 4

-9C - 6S = -15.90

8C + 6S = 15

_____________

-C = -0.90

C = $0.90

substitute C = $0.90 to any of the equations

3C + 2S = 5.30

3(0.90) + 2S = 5.30

2.70 + 2S = 5.30

2S = 5.30 - 2.70

2S = 2.60

S = $1.30