AMC - Basic Equations

This is one of those ones where some of your variables have certain restrictions, so you can use that to intuitively find the answer.



So we have:

1/4 m + 1/6 c = 8
m + c = 8p

We know that p has to be an integer, and m, c, p are all positive. We can get each in terms of p:

P = 6 - 1/16 m = 4 + 1/24 c

Since m c and p are positive, and P is an integer, we can see that P > 4 and P < 6 . Thus, P = 5. In fact, we could also find out that there are 16 ounces of milk and 24 ounces of coffee, too. Nice! Easy like sunday morningggggg.

No political talk from me. I can't vote, and it has nothing to do with competition math. =D