SOLUTION: Algebra.com has been a God send. I have lost many, many hours of family time because of this Algebraic story problem. Any assistance would be greatly apprecited. A cookie compan

Question 16754: Algebra.com has been a God send. I have lost many, many hours of family time because of this Algebraic story problem. Any assistance would be greatly apprecited.
A cookie company makes three kinds of cookies, oatmeal raisin, chocolate chip, and shortbread, packaged in small, medium, and large boxes. The small box contains 1 dozen oatmeal raisin and 1 dozen chocolate chip; the medium box has 2 dozen oatmeal, 1 dozen chocolate chip, and 1 dozen shortbread; the large box contains 2 dozen oatmeal raisin, 2 dozen chocolate chip, and 3 dozen shortbread. I you require 15 dozen oatmeal raisin, 10 dozen chocolate chip, and 11 dozen shortbread cookies, how many of each size box should you buy?
Thank you very much.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Well in my first attempt, I tried to get the largest number of large boxes that would not give more cookies than required, which is 3 large boxes. However, this did not seem to be working out, so I dropped down to 2 large boxes, which would be 4 oatmeal, 4 choc chip, 6 shortbread.

This leaves a need for 11 oatmeal, 6 choc chip, 5 shortbread.

For this, you can order 5 medium boxes, providing 10 oatmeal, 5 choc chip, 5 shortbread. You still need 1 oatmeal, 1 choc chip, which is exactly 1 small box.

In summary, you should order 2 large, 5 medium, and 1 small box.

R^2 at SCC
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