Paint is to be mixed so that the ratio of red paint to white paint is 3 to 2. If Ben wants to make 30 cans of the mixture and all cans hold the same volume of paint, how many cans of red paint will he need?
I want to find the number of cans of red paint, so I will call that x. Then, the number of cans of white paint must be 30 - x, since the total is 30. The ratio of red paint to white paint is 3 to 2, which means that for every 3 cans of red paint, there are 2 cans of white paint. I can write this as a proportion: 3/2 = x/(30 - x). To solve for x, I can cross-multiply and get 3(30 - x) = 2x. Expanding and simplifying, I get 90 - 3x = 2x, or 90 = 5x. Dividing both sides by 5, I get x = 18. This means that Ben needs 18 cans of red paint and 30 - 18 = 12 cans of white paint. 