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.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?