You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40.

You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?

First let’s define a shirt as X and pants as Y!

In the first scenario, the equation will be 3X + Y =$32

In the second scenario, the equation will be 2X + 3Y = $40  

Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!

3X + Y= $32—> subtract 3X on both sides of the equation  

-3X.        - 3X

Net result: Y= 32- 3X

Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable  

2X + 3(32-3X) = $40

2X + 96 - 9X = $40 —> simplify the equation  

-7X + 96 = $40 —> substrate 96 from both sides  

-7X = -56 —> divide both sides by -7  

X= 8  

Now reinsert 8= X into 3X + Y = $32

3(8) + Y = $32

24+ Y = $32 —> substract 24 from both sides

y = 8

ANSWER: X= 8, Y= 8

If I am wrong I am sorry >_<

The shirts cost $8 each and the pants cost $8 each.

Step-by-step explanation:

Let’s represent them by equations:

For you: 3x+y=32

For your friend: 2x+3y=40

Let’s simplify your equation:

y=32-3x

Now we can put it into the second equation, since we now know what y equals.

2x+3(32-3x)=40

2x+96-9x=40

Subtract 96 from both sides

2x+-9x=-56

-7x=-56

Divide by -7 on both sides

x=8

So x is 8.

Now we know what x equals, so we can substitute the 8 into the 1st equation:

3(8)+y=32

24+y=32

Subtract 24 from both sides

y=8

The shirts cost $8 each and the pants cost $8 each.