Question

If it takes you the same amount of time to wash 30 cups as it does to wash 45 plates, how many cups could you wash in the same amount of time it takes to wash 15 plates?

Answer 1

To determine how many cups can be washed in the same amount of time it takes to wash 15 plates, when it is known that washing 30 cups equals the time to wash 45 plates, a proportion is used. The proportion is 30/45 = x/15. We find that x, which represents the number of cups, is 10.

Step-by-step explanation:

To solve the problem of how many cups you could wash in the same amount of time it takes to wash 15 plates, given that washing 30 cups is equivalent in time to washing 45 plates, you can set up a proportion. The proportion to solve is as follows:

• Let x be the number of cups that can be washed in the time it takes to wash 15 plates.
• The ratio of cups to plates when washing 30 cups is the same as 45 plates, which is 30/45.
• Now, set that ratio equal to the ratio of x cups to 15 plates, which is x/15.

So, our proportion is 30/45 = x/15.

To find x, we cross-multiply:

30 x 15 = 45 x x

This simplifies to:

450 = 45x

Divide both sides by 45:

x = 10

Therefore, you could wash 10 cups in the same amount of time it takes to wash 15 plates.