Question

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?

Explanation:

Step1: Find the ratio of green to black paint

The original mix is 4 quarts of green with $\frac{2}{3}$ cup of black. Let $g$ be green paint (in quarts) and $b$ be black paint (in cups). The ratio is $\frac{g}{b}=\frac{4}{\frac{2}{3}}$. Simplify this: $\frac{4}{\frac{2}{3}} = 4\times\frac{3}{2}=6$. So the ratio of green to black is 6 quarts per cup.

Step2: Calculate green paint for 4 cups of black

We know the ratio is 6 quarts per cup. For $b = 4$ cups, $g=6\times4 = 24$ quarts.

Answer:

24 quarts