Question

At Gavin's Department Store, Martha and Laura found shirts on sale at one price, shoes on sale at another price, and pairs of pants on sale for a third price. Martha bought 3 shirts, 2 pairs of shoes, and 2 pairs of jeans for $185. Laura bought 1 shirt, 2 pairs of jeans, and 2 pairs of shoes for $120. Find the sale price of each item.

Answer 1

Let shirt price = x
Let shoe price = y
Let pants price = z
3x + 2y + 2z = 185...............(1)
x + 2y + 2z = 120.................(2)
Now subtract equation (2) from equation (1) to eliminate the terms in y and z and get an equation to enable x to be found. Can you do that?

Answer 2

I got X=32.5

Answer 3

Good work, the price of shirts is $32.50 each.
Now there is a problem. There are three unknowns, but only two equations available to solve all of them. When the value for x is substituted in one of these equations we are left with 2y + 2z = 87.5. So trial and error seems to be needed to find a solution, keeping in mind it is given that all the prices are different.

Answer 4

So any two numbers that fit the equation would work?

Answer 5

For example shoes could be $20 each and pants could be $18.75 each?

Answer 6

whoops sorry shoes would be $25

Answer 7

Two numbers that work are $22 each and $21.75 each.

Answer 8

Okay thank you!

Answer 9

You're welcome :)