Question

Sarah wants to make a purple paint mix. To do this she needs to mix 1/2 cup blue

paint with 1/3 cup red paint. If she wants to mix blue and red paint in the same ratio
to make 20 cups of purple paint, how many cups of blue paint and how many cups of
red paint will Sarah need?

Answer 1

To make 20 cups of purple paint, Sarah will need 2 cups of blue paint and 1.33 cups of red paint.

Step-by-step explanation:

To find out how many cups of blue paint and red paint Sarah will need to make 20 cups of purple paint, we can set up a proportion using the given ratios. The ratio of blue paint to red paint is 1/2:1/3. To simplify this ratio, we can multiply both sides by a common denominator of 6, resulting in a ratio of 3/6:2/6. This means that for every 3 parts blue paint, we need 2 parts red paint.

Since Sarah wants to make a total of 20 cups of purple paint, we can divide 20 by the sum of the parts in the ratio (3+2=5) to find the factor for each part. 20/5 gives us a factor of 4. This means that for every 4 parts in the ratio, we need 4 cups of purple paint.

Now we can multiply the factor by each part of the ratio to find the total amount of blue paint and red paint needed. 4 x 3/6 = 2 cups of blue paint, and 4 x 2/6 = 4/3 or approximately 1.33 cups of red paint. Therefore, Sarah will need 2 cups of blue paint and 1.33 cups of red paint to make 20 cups of purple paint.