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?

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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.
To make Jasper Green with 4 cups of black paint, mix 24 quarts of green paint.

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?

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