SOLUTION: P,Q and R are each mixtures of red and white paint. The percentage by volume of red paint in P is 30%. The percentage by volume of red paint in Q is 20%. The mixtures P,Q,and R

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Question 1091902: P,Q and R are each mixtures of red and white paint.
The percentage by volume of red paint in P is 30%.
The percentage by volume of red paint in Q is 20%.
The mixtures P,Q,and R are combined in the proportion 12:5:3 respectively.
If the resulting mixture contains 25% by volume of red paint, what percentage
by volume of mixture R is red paint ?
The answer was given as 13 and 1/3 % . Just asking about the steps to arrive
at this answer. Thank you, Melton Ellis mellis7379@gmail.com
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

If P, Q, and R are mixed in the ratio 12:5:3, then we can let the amounts of P, Q, and R be represented by 12x, 5x, and 3x; that makes 20x the total amount of the mixture.

Let y be the unknown percentage of R. (To avoid having to use fractions, I will work the problem using percents....) Then the amounts of red paint in the three ingredients are
P: 30(12x)
Q: 20(5x)
R: y(3x)

Then the total amount of red paint in the mixture is
30%2812x%29%2B20%285x%29%2By%283x%29+=+360x%2B100x%2B3yx+=+460x%2B3yx

Then since the total amount of mixture is 20x, the percentage of red paint is
%28460x%2B3yx%29%2F20x+=+%28460%2B3y%29%2F20

We know the percentage of red in the final mixture is 25; so
%28460%2B3y%29%2F20+=+25
460%2B3y+=+500
3y+=+40
y+=+40%2F3

The percentage of red paint in R is 40/3, or 13 1/3.