A mixture of 12 grams of vinegar and oil is 40 percent vinegar, where all of the measurements are by weight. How many grams of oil must be added to the mixture to produce a new mixture that is only 25 percent vinegar?

Hello @gregmat and everyone! Can anyone please tell me how to solve this problem using the “Mixture trick”?

Source - GRE Math Review

In my opinion the easiest here is not to use the mixture trick. First, you have to compute how many grams there are of vinegar: 12x0.4=4.8 grams. Next you want a 0.25 solution, thus 4.8/total=0,25. The total is 19.2 grams, thus you have to add 7.2 grams of oil.

If you really want to use the mixture trick, it would be something like this: you have a solution with 0.4 percent vinegar, you add a solution with 0.0 percent vinegar to get the mixture of 0.25. Thus, write 0.0 (on the left), 0.25 (in the middle), and 0.4 (on the right). Then you compute the ratio of the solution you add to the current one: it is 15:25=3:5. Next you set up this equation and cross multiply: 3/5=x/12. X is here the grams of vinegar you have to add, you get 7.2.

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