Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost?

Shirt $ 16

Sweater $ 33

Step-by-step explanation:

Let the cost of each shirt is $ x, and the cost of each sweater is $ y.

Since, cost of each shirt is $ x, the cost of 3 shirts will be $ 3x and cost of 2 shorts will be $ 2x.

Likewise, cost of each sweater is $ y, so the cost of 2 sweaters will be $ 2y and cost of 4 sweaters will be $ 4y.

Andrea was able to buy 3 shirts and 2 sweaters for $114. This means:

Cost of 3 shirts + Cost of 2 sweaters = 114

3x + 2y = 114 Equation 1

She was able to buy 2 shirts and 4 sweaters for $164. This means:

2x + 4y = 164

Dividing both sides by 2, we get:

x + 2y = 82 Equation 2

Subtracting Equation 2 from Equation 1, we get:

3x + 2y - (x + 2y) = 114 - 82

3x + 2y - x - 2y = 32

2x = 32

x = 16

Using the value of x, in Equation 2, we get:

16 + 2y = 82

2y = 66

y = 33

Since, x represents the cost of shirt, the cost of each shirt is $ 16.

y represents the cost of sweater, so the cost of each sweater is $ 33.