A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug

Hi All,

You have to be very careful about your assumptions with this question. You will likely find that doing a little bit of extra work will help you to be sure that you have the correct answer.

From the prompt, we know that we're mixing P ounces of a 60% sugar solution with Q ounces of a 10% sugar solution to form R ounces of a 25% sugar solution. We're asked for the value of P....

Before dealing with the two Facts, I'm going to set up a "weighted average" equation using the above information....

(.6P + .1Q)/(P+Q) = .25

.6P + .1Q = .25P + .25Q
.35P = .15Q
35P = 15Q

P/Q = 15/35 = 3/7 This means that for every 3 ounces of P, we have 7 ounces of Q. However, we don't yet know the exact number of ounces of each we have....

We also know that R = P+Q

Looking at this from an algebraic standpoint, we have 3 variables and 2 equations.....

Fact 1: Q = 455

With this value, and the given ratio for P/Q, we CAN answer the question.
Fact 1 is SUFFICIENT

Fact 2: R = 660

Since we know that R = P+Q and the ratio of P/Q = 3/7, we CAN answer the question. Here's how...

With the given ratio, for every 3 ounces of P, we have 7 ounces of Q. In basic terms, that means that every 10 ounces is 3 ounces of P and 7 ounces of Q. With a total of 660 ounces, we have 66(3) = 198 ounces of P and 66(7) = 462 ounces of Q.
Fact 2 is SUFFICIENT

Final Answer:

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Rich