Question

One part of paint thinner is used to create 5 parts of paint mixture. A painter has 12 oz of paint. How many ounces of thinner by does the painter need in order to use all of the paint in a paint mixture of the same ratio?

a) 2.4 oz
b) 2.5 oz
c) 2.6 oz
d) 2.7 oz

Answer 1

The painter needs 2.4 ounces of paint thinner to mix with 12 ounces of paint to maintain a 1:5 ratio for the paint mixture.

Step-by-step explanation:

To solve this problem, you can set up a proportion using the ratio given for paint thinner to paint mixture. The ratio is 1 part paint thinner to 5 parts paint mixture. If the painter has 12 ounces of paint, and wants to use all of it in a mixture with the same ratio, we can set up the following proportion:

1 part paint thinner : 5 parts paint

is equivalent to

x parts paint thinner : 12 parts paint

To solve for x (the amount of paint thinner), we can cross-multiply:

1*x = 5*12

x = (5*12)/1

x = 60/1

x = 60

Now we need to remember that x is the total number of parts in this ratio, and we need to find out how many ounces of paint thinner equals 1 part out of 6 total parts (since 1 part thinner plus 5 parts paint equals 6 parts total). So, to find the number of ounces of paint thinner (1 part), we divide the total weight by the total number of parts.

x = 60/6

x = 10

Hence, the painter needs 2.4 ounces of paint thinner for a 12-ounce paint mixture at the same ratio.