Question

A certain mixed paint calls for red paint and black paint in a ratio of 8, colon, 18:1. Brooklyn follows the recipe to make 4545 gallons of mixed paint. How many gallons of red paint did she use?
Answer

Answer 1

To determine how many gallons of red paint Brooklyn used, we start by analyzing the given ratio of red to black paint, which is 8:18.

1. First, we simplify the ratio 8:18:
\[
8:18 = \frac{8}{18} = \frac{4}{9}
\]
Thus, for every 4 parts of red paint, there are 9 parts of black paint.

2. Next, we calculate the total number of parts in the mixture:
\[
4 + 9 = 13 \text{ parts}
\]

3. Since Brooklyn is making 4545 gallons of mixed paint, we can find the size of each part by dividing the total amount of paint by the number of parts:
\[
\text{Size of one part} = \frac{4545 \text{ gallons}}{13 \text{ parts}} = 350 \text{ gallons per part}
\]

4. Now, we calculate the amount of red paint used:
\[
\text{Gallons of red paint} = 4 \text{ parts} \times 350 \text{ gallons per part} = 1400 \text{ gallons}
\]

Therefore, Brooklyn used **1400 gallons of red paint**.