Question

Andrea is buying some new shirts and sweaters. She is able to buy 5 shirts and 3

sweaters for $89 or she is able to buy 9 shirts and 8 sweaters for $207. How much
does a shirt cost? How much does a sweater cost?

Answer 1

Answer: Shirt = $7 and Sweater = $18

Explanation:

5 Shirts, 3 sweaters = $89 (1)
9 Shirts, 8 sweaters = $207 (2)

1 Shirt = $?

1 Sweater = $?

Shirts = x

sweaters = y

(1) -> 5x + 3y = 89

(2) -> 9x + 8y = 207

(1) * 8 = 40x + 24y = $712

(2) * 3 = 27x + 24y = $621

(1) single out 24y -> 24y = $712 - 40x

put value of 24 y into (2)

(2) -> 27x + $712 - 40x = $621

Now solve

-13x = $-91

remove negative -> 13x = $91

x = $7

So a shirt is $7

And we can put $7 into (1) at the start -> 5(7) + 3(y) = $89

35 + 3y = $89

3y = $54

y = $18

Hence x = $7 and y = $18

So Shirt = $7 and Sweater = $18