Question

To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used? First, how many gallons of red paint should be used?

Answer 1

To make 20 gallons of purple paint with a red to blue ratio of 5:3, you need 12.5 gallons of red paint and 7.5 gallons of blue paint.

Step-by-step explanation:

The student has asked how many gallons of red and blue paint should be used if they want to mix a particular shade of purple paint in the ratio of 5:3 and need a total of 20 gallons of this shade. To solve this, we can set up a ratio with two parts: one part representing red paint and one part representing blue paint. According to the given ratio of red to blue is 5:3, the total parts will be 5 + 3 = 8 parts. Since 20 gallons is the total amount of purple paint needed, we divide this by the total number of parts to find out how much each part represents in gallons.

To calculate the gallons of red paint, we multiply the volume represented by one part with the number of parts allocated for red paint: (20 gallons / 8 parts) × 5 parts = 12.5 gallons. Therefore, you would need 12.5 gallons of red paint to mix the desired shade of purple.