Question 1091902
<br>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.<br>
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)<br>
Then the total amount of red paint in the mixture is
{{{30(12x)+20(5x)+y(3x) = 360x+100x+3yx = 460x+3yx}}}<br>
Then since the total amount of mixture is 20x, the percentage of red paint is
{{{(460x+3yx)/20x = (460+3y)/20}}}<br>
We know the percentage of red in the final mixture is 25; so
{{{(460+3y)/20 = 25}}}
{{{460+3y = 500}}}
{{{3y = 40}}}
{{{y = 40/3}}}<br>
The percentage of red paint in R is 40/3, or 13 1/3.