SOLUTION: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of 2% alcohol solution with a 7% alcohol solution. What are the quantities of each should he need to use?

Question 1160466: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of 2% alcohol solution with a 7% alcohol solution. What are the quantities of each should he need to use?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A traditional algebraic solution would start something like this:

x = ml of 2% alcohol
100-x = ml of 7% alcohol

The amount of actual alcohol in the two ingredients is 2% of x ml, plus 7% of (100-x) ml; the amount in the mixture is 5% of 100ml:

That equation is easily solved using basic algebra. I leave it to you to do that.

Here is what is almost certainly the fastest and easiest way to solve a mixture problem like this.

Consider the three percentages on a number line -- 2, 5, and 7. Observe that 5 is 3/5 of the way from 2 to 7.

That means 3/5 of the mixture is the 7% alcohol.

3/5 of 100 ml is 60 ml.

ANSWER: 60 ml of 7% alcohol, 40 ml of 2% alcohol.

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