Question

You decide that you want to make a lighter purple paint. You make the new mixture by adding 1/10 cup of white paint for every 2/5 cup of red paint and 1/4 cup of blue paint. How much red paint, blue paint, and white paint do you use to make 3/8 gallon of lighter purple paint?

(7th Grade Accelerated Big Ideas math)
I am stuck! Any help will be really nice. Thank you so much!

Answer 1

Using the given amounts of paint, we end up with

1/10 + 2/5 + 1/4 = 2/20 + 8/20 + 5/20 = 15/20 = 3/4

cup of purple paint.

But you want to make 3/8 gallons of purple paint. Convert this amount to gallons (remember that there are 16 cups to 1 gallon) :

(3/4 cup) • (1 gal) / (16 cups) = 3/64 gal

and this is 1/8 of 3/8, since 1/8 • 3/8 = 3/64. This means you need 8 times as much whit, red, and blue paint to get the amount you want.

So, you should use

8 • 1/10 = 8/10 = 4/5 cup white paint

8 • 2/5 = 16/5 = 3 + 1/5 cups red paint

8 • 1/4 = 8/4 = 2 cups blue paint