Not really sure how to find these

Question

How many gallons of a 12% indicator solution must be mixed with a 20% indicatior solution to get 10 gallons of a 14% solution 

Answer 1

Another way to think of this is say I need x% of the 12% solution and 1-x% of the 20% solution to get a 14% solution. This yields .12x + (1-x).2=.14, or x = 75%. So a mix of 75% of the 12 % solution plus 25% of the 20% solution will gives us 14% mix. So I need 7 gallons and 2 quarts of the 12% solution and 2 gallons and 2 quarts of the 20% solution.

Answer 2

Hi Steve,

We start by aiming for 10gal of 14% indicator solution (0.14).
Then we know that x liters of the 12% solution (0.12) + y liters of the 20% solution (0.2) must equal 10gal, so x+y=10, which we can rearrange to say y=10-x.
This gives us: 10(0.14)=x(0.12)+(10-x)(0.2)
If we solve for x, we'll know how much of the 12% indicator must be used and 10-x will be the amount of 20% indicator.