SOLUTION: How many ounces of a 15​% alcohol solution must be mixed with 4 ounces of a 20​% alcohol solution to make a 17 ​% alcohol​ solution? The number of ounces of the ​% alco

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Question 1163666: How many ounces of a 15​% alcohol solution must be mixed with 4 ounces of a 20​% alcohol solution to make a 17 ​% alcohol​ solution?
The number of ounces of the ​% alcohol solution that needs to be mixed is
nothing ounces.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You are mixing x ounces of 15% alcohol and 4 ounces of 20% alcohol to get (x+4) ounces of 17% alcohol:

.15%28x%29%2B.20%284%29+=+.17%28x%2B4%29

Solve using basic algebra (I leave that to you).

If a formal algebraic solution is not required, here is a quick informal solution method.

You are starting with 20% alcohol and adding 15% alcohol; the more you add, the closer the mixture gets to 15%.

You stop adding the 15% alcohol when the percentage of the mixture gets to 17%.

17% is 3/5 of the way from 20% to 15%. (If it helps, picture the three percentages 20, 17, and 15 on a number line.)

That means 3/5 of the mixture is what you are adding.

So the 4 ounces you started with is 2/5 of the mixture; that means 3/5 of the mixture is 6 ounces.

So the amount of 15% alcohol you added is 6 ounces.

ANSWER: 6 ounces of 15% alcohol should be used.

Of course that is the answer you should get if you finish solving the problem by the algebraic method shown above.