Question

Brian measured the amount of water that evaporated over a period of time from a container holding w ounces of water, where w is greater than $12$. By the end of the first day, the cup had lost $2$ ounces of water. By the end of the $7^{th}$ day, the cup had lost an additional $8$ ounces of water. By the end of the ${11}^{th}$ day, the cup had lost half of the water that remained after the $7^{th}$ day. Which of the following represents the remaining amount of water, in ounces in Brian's container at the end of the ${11}^{th}$ day?

• A. $\frac{w-2}{8}$
• B. $\frac{w-2}{2}-10$
• C. $\frac{1}{2}w-10$
• D. $\frac{w-10}{2}$

Answer 1

The correct option is D $\frac{w-10}{2}$

If $w=20$, then Luciano's cup has $20-2=18$ ounces at the end of day 1.

At the end of $7$ days, Luciano's cup would have $18-8=10$ ounces.

After $11$ days, Luciano's cup would hold $10-5=5$ ounces.

Plug in $20$ for $w$ in the answer choices to see which answer is equal to the target number of $5$.

Choice (A) becomes$\frac{20-2}{8}=\frac{18}{8}=2.25$.

This does not match the target number of $5$, so eliminate (A).

Choice (B) becomes $\frac{20-2}{2}-10=\frac{18}{2}-10=9-10=-1$.

Eliminate (B). Choice (C) beccome$\frac{1}{2}\times 20-10=10-10=0$.

Eliminate (C). Choice (D) becomes$\frac{20-10}{2}=\frac{10}{5}=5$.

This matches the target number; therefore, the correct answer is (D).

Then answer is $\frac{w-10}{2}$