Question

Andrea is buying some new shirts and sweaters. she is able to buy 3 shirts and 7 sweaters for $137 or she is able to buy 8 shirts and 10 sweaters for $218. how much does a shirt cost? how much does a sweater cost?

Answer 1

Answer:

$33

Step-by-step explanation: ( pls brainiest)

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.