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

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(13200) (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

Then since the total amount of mixture is 20x, the percentage of red paint is

We know the percentage of red in the final mixture is 25; so

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