How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 12 gallons of 30% alcohol solution?

Question

_______ gallons of 20% alcohol solution

 

 

_______ gallons of 50% solution

Answer 1

This is just a system of two equations in two unknowns.
x = number gallons 20% alcohol solution
y = number gallons 50% alcohol solution

Equation in number of gallons
x + y = 12

Equation in concentration
0.2x + 0.5y = 0.3(12)

I multiply the concentration equation through by 100 to get rid of the decimals.
2x + 5y = 36

There are a number of ways you can solve this from there. If I multiply the number of gallons equation through by 2,

2x + 2y = 24

Subtract the number of gallons result from the concentration result and get

3y = 12

So y=4 gallons and x=8.

 

Your sanity check is to pop the answer into both equations and see if your result is true.