Question

A paint mixer wants to mix paint that is 30% gloss with paint that is 15% gloss to make 3.75 gallons of paint that is 20% gloss. How many gallons of each paint should the paint mixer mix together?

Answer 1

• 1.25 gallons of 30% gloss and 2.5 gallons of 15% gloss

Explanation:

Gloss content is same at the input and output.

Let 30% gloss is x gallons, then 15% gloss is (3.75 - x) gallons.

We have the following equation:

• 0.3x + 0.15(3.75 - x) = 0.2*3.75
• 0.3x + 0.5625 - 0.15x = 0.75
• 0.15x = 0.75 - 0.5625
• 0.15x = 0.1875
• x = 0.1875/0.15
• x = 1.25 gallons

Amount of 15% gloss:

• 3.75 - 1.25 = 2.5 gallons

30% gloss is 1.25 gallons and 15% gloss is 2.5 gallons