DerekLin
A certain solution that is 30 percent acid is obtained by mixing x gallons of a 20 percent acid solution with y gallons of a 60 percent acid solution, where the percents are according to volume. How many gallons of the 60 percent acid solution must be used to obtain 10 gallons of the 30 percent acid solution?
A. 0.75
B. 2.5
C. 3.3
D. 4.0
E. 5.0
Volume of the solution that is 30% acid = \(x + y\)
Amount of acid in that solution = \(\frac{30}{100}(x+y) = 0.3x + 0.3y\)
The amount of acid in the solution that is 30% acid = Volume of acid in the solution that is 20% acid + Volume of acid in the solution that is 60% acid
\(0.3x + 0.3y = 0.2x + 0.6y\)
\(0.1x = 0.3y\)
\(\frac{x}{y} = \frac{3}{1}\)
Hence, for every 1 part of 'y' we have 3 parts of 'x'.
The number of gallons of the 60 percent acid solution must be used to obtain 10 gallons of the 30 percent acid solution = \(\frac{1}{4} * 10 = 2.5\)
Option B