Three people go to a store where there is a sale. One person buys two shirts, one pair of pants and one sweater. The second person buys one shirt, two pairs of pants and two sweaters. The third person buys three shirts and four pairs of pants. Find the price of each item if the first person spent $155 and the second and third person spent $235 each.

Thanks for your help and time
geocee

This is a system of three equations with three variables, so let's start by assigning variable names and writing out the equations.

Let t = the number of shirts, p = the number of pairs of pants, s = the number of sweaters.

The first person buys two shirts, one pair of pants and one sweater and pays $155, so that means:

2t + p + s = 155

The second person buys one shirt, two pairs of pants and two sweaters
and pays $255, so:

t + 2p + 2s = 255

The third person buys three shirts and four pairs of pants, spending $235, so:

3t + 4p = 235

To solve these equations, we first try to eliminate one variable. We
can choose any one, so let's eliminate s (sweaters). That means we
solve the first and second equation for s, then make them equal to
each other:

2t + p + s = 155, therefore s = 155 - p - 2t
t + 2p + 2s = 255, therefore s = (255 - 2p - t) / 2

So, 155 - p - 2t = (255 - 2p - t) / 2. Let's simplify:

155 - p - 2t = (255 - 2p - t) / 2
310 - 2p - 4t = 255 - 2p - t
55 = 3t
t = 55/3

Now that you have the price of the shirts, you can substitute that
into the third person's purchases to find the price of the pants, then
use those to get the sweater price. Don't forget to check your
figures by substituting them into all the initial equations and
ensuring that you get the right totals.

If you want another example, take a look at this earlier problem.

Hope this helps,
Stephen La Rocque.

Geocee wrote back

Hello Sue
I have listed below both my previous question and your answer for which I thank you. I don't understand however about the second person paying $255 when the question states both the second and third persons spent $235. Can you explain?

Thanks
geocee

Geocee,

Thanks for pointing out my error. I mistakenly wrote $255 when I shoould have written $235. The technique is however correct so if you change the $255 to $235 you can follow the steps to obtain the correct answer.

Stephen La Rocque>