Question

Please help me solve the problem: A mixture of 12 ounces of vinegar and oil is 40 percent vinegar by weight. How many ounces oil must be added to the mixture to produce a new mixture that is only 25 percent vinegar?

Answer 1

12 oz @ 0.4 = 4.8 oz vinegar.
12 oz @ 0.6 = 7.2 oz oil.

You want 25% of some volume to be 4.8 oz vinegar.
0.25 X = 4.8
X = 19.2 total volume.
You had 12 oz; therefore, you must add 19.2 - 12.0 oz oil or you must add 7.2 oz oil to make a final volume of 19.2 oz.

You can check it to see if it is right.
4.8 oz vinegar + 7.2 oz oil (initially) + 7.2 oz oil added to make 19.2 oz total.
vinegar is 4.8/19.2 = 0.25
oil is 14.4/19.2 = 0.75
Check my thinking. Check my work.