SOLUTION: If Solution A contains 59% nitrogen and Solution B contains 94% nitrogen. How much of each solution should be mixed in order to create 70 cups of a solution that contains 69% nitro

Question 1126843: If Solution A contains 59% nitrogen and Solution B contains 94% nitrogen. How much of each solution should be mixed in order to create 70 cups of a solution that contains 69% nitrogen?
Found 2 solutions by addingup, greenestamps:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
A + B = 70 therefore B = 70 - A
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0.59A + 0.94(70 - A) = 0.69(70)
0.59A + 65.8 - 0.94A = 48.3
-0.35A = -17.5 divide, remember -/- = +
A = 50
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So, 50 cups of the 59% solution should be mixed with 70 - 50 = 20 cups of 94% solution to get 70 cups of a 69% solution
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Here is a method for solving this kind of problem without the need to write and solve an algebraic equation.

If you understand it, you will solve this kind of problem much faster and with much less work than with the standard algebraic method.

Think of starting with the 59% solution and adding some of the 94% solution, stopping when the mixture is 69%.

69% is 10/35 of the distance from 59% to 94% (do some simple mental arithmetic).

That means 10/35 = 2/7 of the mixture must be the 94% solution you were adding.

2/7 of 70 cups is 20 cups.

ANSWER: 20 cups of the 94% solution, 50 cups of the 59% solution.
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