4. Mr. V taught me how to make green paint. He told me to mix yellow and blue. I found that the shade of green I liked best used a ratio of $$ 4: 7 $$, yellow to blue. I want to make 22 gallons of green paint. How many gallons of each color do I need? 4.

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1. Let the number of gallons of yellow be $$ y $$ and the number of gallons of blue be $$ b $$.
2. The total amount of paint is given by: 
   $$
   y + b = 22
   $$
3. The ratio of yellow to blue is $$ 4:7 $$, which means:
   $$
   \frac{y}{b} = \frac{4}{7}
   $$
4. Express $$ y $$ in terms of $$ b $$:
   $$
   y = \frac{4}{7}b
   $$
5. Substitute $$ y = \frac{4}{7}b $$ in the equation $$ y + b = 22 $$:
   $$
   \frac{4}{7}b + b = 22
   $$
6. Combine the terms:
   $$
   \frac{4}{7}b + \frac{7}{7}b = \frac{11}{7}b = 22
   $$
7. Solve for $$ b $$:
   $$
   b = 22 \times \frac{7}{11} = 14
   $$
8. Substitute $$ b = 14 $$ back into the expression for $$ y $$:
   $$
   y = \frac{4}{7} \times 14 = 8
   $$

Thus, you need $$ 8 $$ gallons of yellow and $$ 14 $$ gallons of blue.
You need 8 gallons of yellow paint and 14 gallons of blue paint.

4. Mr. V taught me how to make green paint. He told me to mix yellow and blue. I found that the shade of green I liked best used a ratio of \( 4: 7 \), yellow to blue. I want to make 22 gallons of green paint. How many gallons of each color do I need? 4.

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