M gallons of a p% salt solution must be mixed up with G gallons of a q% salt solution to produce an r% solution. Which of the following best describes how to find the value of r? (This question is driving me insane.)

(A) (p + g) / (M + G) = r / 100

(B) (0.01p + 0.01q) / (M + G) = r / 100

(C) 0.01p / M + 0.01q / G = r / 100

(D) (0.01M + 0.01G) / (M + G) = r / 100

(E) (0.01pM + 0.01qG) / (M+G) = r / 100

Break the parts down.

“M gallons of a p% solution”: M\times\dfrac{p}{100}

“G gallons of a q% solution”: G\times\dfrac{q}{100}

The r% solution will be M + G gallons, so: (M + G)\times\dfrac{r}{100}

The setup, then, is this:

M\times\dfrac{p}{100}+G\times\dfrac{q}{100}=(M + G)\times\dfrac{r}{100}

That simplifies to :

0.01Mp + 0.01Gq=(M + G)\dfrac{r}{100}

\dfrac{0.01Mp + 0.01Gq}{M+G}=\dfrac{r}{100}

This really isn’t a realistic SAT question, though. If you got this out of an SAT prep book, you’re being led astray.

Comments (1)

Thanks for the solution (much clearer than the one in the book where this came from). It is from an SAT prep book meant to deal with level 4, 5, and beyond questions, really just for some extra practice to get those final points. (Although your book did raise my math score from around a 620 to a 760, which I appreciate very much =) .) I know more practice from regular cb tests would probably be better, but this book has been lying around for a year so I decided just to go for it 😛

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