Question

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

Answer 1

Red paint = 12.5 gallons

Blue paint = 7.5 gallons

Explanation:

The given ratio of red paint to blue paint is:

• red : blue = 5 : 3

Let x be the number of gallons of purple paint.

Therefore, the expression for each color of paint needed per x gallons of purple paint is:

`\implies \textsf{Red\;paint $=(5)/(8)x$}`

`\implies \textsf{Blue\;paint $=(3)/(8)x$}`

To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:

`\implies \textsf{Red\;paint $=(5)/(8) * 20=(100)/(8)=12.5$}`

`\implies \textsf{Blue\;paint $=(3)/(8)* 20=(60)/(8)=7.5$}`

Therefore, the number of gallons of paint that should be used are:

• Red paint = 12.5 gallons
• Blue paint = 7.5 gallons