The cost of five boxes of envelope and 5 boxes of paper is $25.95. Two boxes of envelopes and 6 boxes is $22.38. How much would it cost to buy one box of each?

Let's say x = envelopes and y = paper

We can create a system of equations

5x + 5y = 25.95

2x + 6y = 22.38

Now we will try to eliminate one of the variables

Let's eliminate x. In order to do that, we need the x's in both equations to have the same coefficient. We can multiply the first equation by two and the second equation by 5.

10x+10y = 51.9

10x + 30y = 111.9

Then we subtract the top equation from the bottom (or vice versa). And we will get:

-20y = - 60

20y = 60

y = 3

Now that we have found the price of a box of paper, we can now plug that y value into either equation and find the value for x

2x + 6 (3) = 22.38

2x = 4.38

x = 2.19

We can now check our work by plugging in both values to see if we get the right answer

5 (2.19) + 5 (3) = 25.95

10.95 + 15 = 25.95

25.95 = 25.95

Our math works out, so we got the right answer:

1 box of envelopes costs $2.19

1 box of paper costs $3