Answer:
Shirt $ 16
Sweater $ 33
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.