SOLUTION: We would like to create 20 gallons of solution that is 25% acid. How many gallons each, of a 10% acid solution and a 30% acid solution would we mix?

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Question 1112659: We would like to create 20 gallons of solution that is 25% acid. How many gallons each, of a
10% acid solution and a 30% acid solution would we mix?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
25% target is three-quarters of the way from 10% to 30%.
25% is closer to 30% than it is to 10%, so need more of the 30% than the 10%.

, gallons of the 30% acid

, gallons of the 10% acid.

Does that pair of results work?

------true

The answer found works.
5 gallons of the 10%
and 15 gallons of the 30%

Answer by ikleyn(52786) (Show Source):
You can put this solution on YOUR website!
.
You can solve the problem algebraically and/or intuitively.

Intuitive solution is this:

On each gallon of the 10% solution take 3 gallons of the 30% solution. It works, since = = 0.25 = 25%. Thus you get 5 groups/packages each containing (1 gallon of the 10% solution PLUS 3 gallons of the 30% solutions), which gives you 5 gallons of the 10% solution AND 15 gallons of the 30% solutions, in all.

Algebraic solution is this:

= 0.25. saying that the concentration of the mixture is 25% = 0.25. The steps to solve it are 0.1x +0.3*(20-x) = 0.25*20 0.1x + 6 - 0.3x = 5 -0.2x = 4 - 5 = -1 ====> x = = 5. You get the same answer: 5 gallons of the 10% solution and (20-5) = 15 gallons of the 30% solution.

Solved.