It's Halloween, and the triplets will be coming to my door, expecting candy. Ryan loves red candy (R), Giles loves green (G), and Bahara is a fan of blue (B).
I go to the store to get candy. The only R/G/B candies are Hurties (H), Marsh (M), and Nessy (N). Each company makes bags containing a particular number and color mixture as follows:
Hurties Marsh Nessy
# Red: 2 4 12
# Green: 5 5 7
# Blue: 6 7 3
------- -- -- --
# Total: 13 16 22
I figure I want to give 100 pieces of candy to each of the triplets,
and I really only want to give each triplet candies of their favorite
color.
Is there a way to buy exactly 300 pieces of candy, which can be divided up by color to make each of the triplets happy? In other words, how many bags of H, M and N candy should I buy?
I give up, show me the solution.