A mixture contains forty ounces of glycol and water and is ten percent glycol. If the mixture is to be strengthened to twenty-five percent, how much glycol is to be added?

4 oz

8 oz

10 oz

Question

A mixture contains forty ounces of glycol and water and is ten percent glycol. If the mixture is to be strengthened to twenty-five percent, how much glycol is to be added?



4 oz

8 oz

10 oz

whpalmer4 · Answer

It works well with many of these problems to think in terms of the "active" ingredient and the total volume.

40 oz of solution that is 10% glycol contains 10%*40 = 4 oz of glycol.

The final solution will be 40 oz + however much glycol you add, and will satisfy the relationship that 25%  = (current glycol + added glycol)/(total volume) and total volume = current volume + added glycol

whpalmer4 · Answer

If you write that in equation terms, with $x$ as the amount of glycol to be added:

$$0.25 = \frac{4+x}{40+x}$$Solve for $x$

Be sure to check your answer to verify that it is correct!