Question

A paint mixer wants to mix paint that is 15% gloss with paint that is 30% gloss to make 5 gallons of paint that is 20% gloss.

How many gallons of each paint should paint mixer mix together?

a. The paint mixer should use 1 2/3 gallons of 15% gallons and 3 1/3 gallons of 3 gloss paint.
b. The paint mixer should use 3 gallons of 15% gloss paint and 2 gallons of 30% gloss paint.
c. The paint mixer should use 2 gallons of 15% gloss paint and 3 gallons of 30% gloss paint.
d. The paint mixer should use 3 1/3 gallons of 15% gloss paint and 1 2/3 gallons of 3 gloss paint.

Answer 1

Answer: d. The paint mixer should use 3 1/3 gallons of 15% gloss paint and 1 2/3 gallons of 30% gloss paint.

Explanation:

To make a paint of 20% gallon, the quantity of gloss in 5 gallons of 20% gloss.

0.2 × 5 = 1 gallon.

To get 1 gallon from a combination of 15% gallon and 30% gallon.

Let x rep the volume of 15% gallon.

The volume of 30% gallon can be given as;

5-x.

And we can interpret to form the equation below.

0.15x + 0.3(5-x) = 1

0.15x+1.5-0.3x = 1

-0.15x = 1-1.5 = -0.5

x = -0.5/-0.15

x = 10/3 = 3 1/3

5-x = 5-10/3 = 5/3 = 1 2/3

Therefore, the gallons of 15% = 3 1/3

And the gallons of 30% = 1 2/3