Question

A mixture of paint calls for 1/3 cups of red paint and 3/4 cups of yellow paint. If there were 4 cups of red paint added to the mixture, how many cups of yellow paint would need to be added to keep a constant rate of proportionality?

a) 9/4 cups of yellow paint
b) 4/3 cups of yellow paint
c) 2/3 cups of yellow paint
d) 3/2 cups of yellow paint

Answer 1

To keep a constant rate of proportionality, you would need to add 9/4 cups of yellow paint.

Step-by-step explanation:

To keep a constant rate of proportionality, we need to determine how many cups of yellow paint would need to be added if 4 cups of red paint are added to the mixture. In the original mixture, the ratio of red paint to yellow paint is 1/3 cups to 3/4 cups. We can set up a proportion to solve for the cups of yellow paint:

1/3 cups / 3/4 cups = 4 cups / x cups

Cross multiplying, we get:

(1/3) * x = (3/4) * 4

Simplifying, we find that:

x = (3/4) * 4 / (1/3)

x = 9/4

Therefore, the amount of yellow paint that would need to be added to keep a constant rate of proportionality is 9/4 cups.