Test 1 No Calculator #7
This is a really interesting question. The SAT is basically trying to psych you out with the complexity of the equation provided. However, note that all you’re asked to do is rearrange it to get P all by itself—that’s what it means to get P in terms of m, r, and N. So let’s rewrite the original equation a bit more simply:
![\begin{align*}m&=\dfrac{\text{[apple][banana]}}{\text{[banana]}-1}P\end{align*}](https://i0.wp.com/pwntestprep.com/wp-content/ql-cache/quicklatex.com-9c66e1a7020f8305d2e4ee750eba359b_l3.png?resize=190%2C43&ssl=1)
See what I’m doing there? Because I can move those elements of the equation around in big chunks by multiplying and dividing, it doesn’t really matter what they are. The only question is: what do I need to do to get P by itself? And the answer to that is I need to move the big complicated fraction over to the other side of the equals sign.
![\begin{align*}m&=\dfrac{\text{[apple][banana]}}{\text{[banana]}-1}P\\\\(\text{[banana]}-1)m&=\text{[apple][banana]}P\\\\\dfrac{\text{[banana]}-1}{\text{[apple][banana]}}m&=P \end{align*}](https://i0.wp.com/pwntestprep.com/wp-content/ql-cache/quicklatex.com-2e67e5c7a49e59a2be2045485da2f088_l3.png?resize=329%2C188&ssl=1)
That wasn’t so bad, right? The answer choice you seek is B—the one with the original fraction flipped and on the other side of the equals sign from P.