To make a shade of paint called Jasper Green, mix 4 quarts of green paint with \( \frac{2}{3} \) of a cup of black paint. How much green paint should be mixed with 4 cups of black paint to make Jasper Green?

To find out how much green paint should be mixed with 4 cups of black paint to make Jasper Green, we can set up a proportion based on the given information. Let's denote the amount of green paint needed as \( x \) quarts. From the given information, we know that 4 quarts of green paint is mixed with \( \frac{2}{3} \) of a cup of black paint to make Jasper Green. This can be represented as: \[ \frac{4 \text{ quarts of green paint}}{\frac{2}{3} \text{ cup of black paint}} = \frac{x \text{ quarts of green paint}}{4 \text{ cups of black paint}} \] Now, we can solve for \( x \) to find out how much green paint should be mixed with 4 cups of black paint to make Jasper Green. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{4}{\frac{2}{3}}=\frac{x}{4}\) - step1: Divide the terms: \(6=\frac{x}{4}\) - step2: Swap the sides: \(\frac{x}{4}=6\) - step3: Cross multiply: \(x=4\times 6\) - step4: Simplify the equation: \(x=24\) The amount of green paint needed to be mixed with 4 cups of black paint to make Jasper Green is 24 quarts.