Question 1039804: Hi,
I'm stuck on this problem and would appreciate any help given:
You mix 2/5 cups of red paint for every 1/4 cup of blue paint to make 1 5/8 gallons of purple paint.
a) how much red and blue paint do you use?
B) 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, blue, and white paint do you use to make 3/8 gallon of lighter purple paint?
Thank you so much. This is quite a long problem so I appreciate any and all efforts taken to solve it. Thanks.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You mix 2/5 cups of red paint for every 1/4 cup of blue paint to make 1 5/8 gallons of purple paint.
a) how much red and blue paint do you use?
(2/5)gallon + (1/4)gallon = 13/20 gallon
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# of 13/20 gallons in 1 5/8 gallons::
(1 5/8)/(13/20) = (13/8)/(13/20) = 20/8 = 2.5 (13/20) gallons
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2.5*(2/5)red = 2.5*0.4 red = 1 gallon of red paint
2.5*(1/4)blue = 5/8 gallon of blue
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B) 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, blue, and white paint do you use to make 3/8 gallon of lighter purple paint?
(1/10)gallon + (2/5)gallon + (1/4)gallon = 15/20 gallons
# of 15/20 gallons in (3/8) gallon:
(3/8)/(15/20) = (3/8)(20/15) = (1/2)(5/5) = 1/2 gallons
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(1/2)(1/10) = 1/20 gallon of white
(1/2)(2/5) = 1/5 gallon of red
(1/2)(1/4) = 1/8 gallon of blue
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Cheers
Stan H.
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