A chemist must prepare 350ml of a chemical solution made up of two parts alcohol and three parts acid. How much of each should be used?

This is the solution to simple "Applications Of Equations".

Now the solution: Let n be the number of milliliters in each part. The picture above shows the solution. From the diagram, we have

2n+3n = 350

5n = 350

n = 350/5 = 70

But n = 70 is not the answer to the original problem. Each part has 70 ml.

The amount of alcohol is 2n = 2(70) = 140, and the amount of acid is 3n = 3(70) = 210.

Thus, the chemist should use 140ml of alcohol and 210ml of acid are the answers to this simple equation problem using two variables.

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55 Comments

William Laughlin

Jeanzi Nancy Szur, Sorry, but thirds are not involved here. The ratio is 2 to 3 equaling 5 parts. It is two fifths plus three fifths or 40% and 60%.

JRW

I am quite surprised that over one third cannot do simple arithmetic. Is the problem, as William Laughlin says, to understand that the ratio of alcohol:acid is 2:3? Or is it the inability to do 2/5 X 350?

Howard Groopman

Simple arithmetic that 38% either didn't know how to do, or didn't want to take the time to do.

Jerry Kimball

Ignores the effect of volume contraction due to molecule size...think of a bucket of golf balls, quite a lot of sand can be poured into the bucket due to the relative size of golf ball vs sand grain size.