 # Problem of the Week Problem A and Solution Bean There; Done That

## Problem

Suppose you want to make a four-bean salad using green beans, wax beans, kidney beans, and garbanzo beans. When you weigh the ingredients you notice the following:

• In total, the mass of all the beans in the salad is $$1$$ kg.

• The sum of the mass of the garbanzo beans and the mass of the green beans make up half of the total mass of the beans in the salad.

• The masses of the garbanzo beans and the green beans are the same.

• The mass of the wax beans is $$235$$ g. ## Solution

We know that $$1$$ kg equals $$1000$$ g. Half the total mass of the beans is $$1000 \div 2 = 500$$ g. So the total mass of the garbanzo beans and the green beans is $$500$$ g. Since the remaining salad is made up of the other two kinds of beans, the total mass of the wax beans and the kidney beans must also be $$500$$ g.

Since the masses of the garbanzo beans and the green beans are the same, then each mass is equal to $$500 \div 2 = 250$$ g.

Since the mass of the wax beans is $$235$$ g, then the mass of the kidney beans must be $$500 - 235 = 265$$ g.

• $$250$$ g of garbanzo beans
• $$250$$ g of green beans
• $$235$$ g of wax beans
• $$265$$ g of kidney beans