Question

Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $117, or she is able to buy 2 shirts and 4 sweaters for $158. How many dollars does a shirt cost? How many dollars does a sweater cost?

Answer 1

Explanation:

Let the cost of a shirt be "s" and the cost of a sweater be "w". We can set up a system of two equations to represent the given information:

3s + 2w = 117

2s + 4w = 158

We can use elimination method to solve for "s" and "w". Multiplying the first equation by 2 and subtracting the second equation from it, we get:

6s + 4w - 2s - 4w = 234 - 158

4s = 76

s = 19

Substituting this value of "s" into either of the original equations, we get:

3(19) + 2w = 117

57 + 2w = 117

2w = 60

w = 30

Therefore, a shirt costs $19 and a sweater costs $30.