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
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