Expert: Steve Holleran - 3/20/2008

Question
I am trying to teach myself algebra just for the heck of it, I am having trouble with this problem,   if the math club spends $20 and buys 3 cases of juice and 1 case of water, and the science club buys 1 case of juice and 2 cases of water, for a total of $15,       how much are the juice and the water per case?

Answer
Hi Bill,

Okay, call cases of juice j and cases of water w.

Then you have these two equations:

                   3j + 1w = 20

                   1j + 2w = 15

Multiply the top equation by -2 and add it to the second:

                  -6j - 2w = -40

                   1j + 2w = 15
                 -------------------

                  -5j = -25   so j = 5.  Then using the first equation,

  3(5) + 1w = 20  so 15 + w = 20 and w = 5 also.

Looks like juice and water are going for $5 per case each.

Steve