SOLUTION: You mix 1/4 cup of red paint for every 1/2 cup of blue paint to make 3 Gallons of purple paint. A. How much red paint did you use? How much blue paint did you use? B. You decide

Algebra ->  Radicals -> SOLUTION: You mix 1/4 cup of red paint for every 1/2 cup of blue paint to make 3 Gallons of purple paint. A. How much red paint did you use? How much blue paint did you use? B. You decide      Log On


   

Question 1178336: You mix 1/4 cup of red paint for every 1/2 cup of blue paint to make 3
Gallons of purple paint. A. How much red paint did you use? How much blue
paint did you use?
B. You decide that you want to make a lighter purple paint.
You make the new mixture by adding 1/4 cup of white paint for every 1/4 cup
of red paint and 1/2 cup of blue paint. How much red paint, blue paint and
white paint do you use to make 1 1/2 gallons of the lighter purple color?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of red to blue is (1/4):(1/2).  Multiplying both numbers by 4 gives
(4x1/4):(4x1/2) or 1:2.  Since we ended up with 3 gallons, there was 1 gallon
of red and 2 gallons of blue.

Edwin

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
B. You decide that you want to make a lighter purple paint.
You make the new mixture by adding 1/4 cup of white paint for every 1/4 cup
of red paint and 1/2 cup of blue paint. How much red paint, blue paint and
white paint do you use to make 1 1/2 gallons of the lighter purple color? 
You mix 1/4 cup of white paint for every 1/4 cup of red paint and 1/2 cup of
blue paint to make 1 1/2 Gallons of purple paint. the ratio of
white:red:blue is (1/4):(1/4):(1/2).  Multiplying all 3 numbers by 4 gives
 [4x(1/4)]:[4x(1/4)]:[4x(1/2)] = 1:1:2.  That means that 

1/(1+1+2) = 1/4 of the 1 1/2 gallon is white paint. 
That's (1/4)x(1 1/2) = (1/4)x(3/2) = 3/8 gallons of white paint.

Since there was the same amount of red as white, there was also 3/8 gallons
of red paint.

There is twice as much blue paint as either of the other colors, so there
was 2x(3/8) = 6/8 = 3/4 gallons of blue paint.

To change gallons to cups multiply everything by 16 cups per gallon:

(3/8)x16 = 6 cups of white.
6 cups of red
12 cups of blue.

That gives 6+6+12 = 24 cups of light purple paint and 24รท16 = 24/16 = 3/2 = 
1 1/2 gallons.

Edwin