A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?

Solution:

We'll let p = pans of pasta
We'll let s = sandwich trays

Equation #1     14p + 6s = 64
...because one pan of pasta will serve 14 people, one sandwich tray will serve 6 people and he has 64 people total to serve.

Equation #2       39p + 12s = 150
...because one pan of pasta costs $39 and one sandwich tray costs $12, and he can spend $150.

We could use any of the methods to solve this system, but Linear Combination seems to be the best way for this one.

Multiply the 1st equation by -2 so we can eliminate the s variable.
Now we have:        -28p - 12s = -128
                           +  39p + 12s = 150
                                       11p = 22
                                         p = 2

Substitute 2 back into one of the original equations and solve for s.
14(2) + 6s = 64
28 + 6s = 64
6s = 36
s = 6

Solution:
The caterer should make 2 pans of pasta and 6 sandwich trays.

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