Question

Three piles of 7 beans each are to be made from 10 red, 5 yellow, and 6 green beans. If all of the beans must be used and each stack must contain at least one bean of each color, then what is the maximum number of red beans that can be put in one of the stacks?

Answer 1

The maximum number of red beans that can be put in one of the stacks is 5.

Explanation:

First, Every pile is made with 7 beans, but they need to have at least one bean of each color, so we need to include in the pile minimum one yellow bean and one green bean. If we make a stack with this condition, the stack is going to have: 1 yellow bean, 1 green bean, and 5 red beans.

Additionally, it is necessary to know if there are enough red beans for the other piles. In this case, we have 10 red beans so if we have 5 red beans in one stack, the other two stacks have enough red beans to fulfill with the condition to have at least one red bean.

So, the maximum number of red beans that can be put in one of the stacks is 5.