Jimmy D. answered • 04/18/20

Tutored Math for 2 years

Say you let: x represent hats, y represents shirts, z represent jackets

You have three sets of information/equations and three sets of variables

Set 1: 3x+2y+z=140

Set 2: 2x+2y+2z=170

Set 3: x+3y+2z=180

You want to reduce three equations to two equations by combining any two of the above equations to remove a variable.

In this case, I am taking z out of the picture

Let us do

Set 1 - (Set 2)/2, which gives 2x + y = 55 (Let's call it Combo 1)

&

Set 3 - Set 2, which gives -x + y = 10 (Let's call it Combo 2)

Now, you can combine those two equations in a way to remove either x or y

I'll be taking y out of the picture

So we do

Combo 1 - Combo 2, which gives 3x=45

__x=15__

Now plug x=15 in to any Combo equation that we made to find y.

Let's use Combo 2 with x = 15

-15 + y = 10

__y = 25__

Now plug x = 15 and y = 25 in to any Set equation we originally have to find z

Let's use Set 1 with x = 15 and y = 25

3(15) + 2( 25) + z = 140

45 + 50 + z = 140

95 + z = 140

__z=45__

So hat cost $15, shirt cost $25, and jacket cost $45

Hope that helps!