Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If, instead, Anna takes six CDs from Ben, then both would have the same number of the CDs. What is the total number of CDs that Ben and Anna have?
(A) 42
(B) 30
(C) 72
(D) 18
(E) 36
Solution 1

Let $A$ be the number of CDs that Anna has, and let $B$ be the number of CDs that Ben has. If Anna gives $6 \mathrm{CDs}$ to Ben, then Anna would have $A-6 \mathrm{CDs}$ and Ben would have $B+6 \mathrm{CDs}$, so from the given information, $B+6=2(A-6)$.

If Anna takes $6 \mathrm{CDs}$ from Ben, then Anna would have $A+6 \mathrm{CDs}$ and Ben would have $B-6$ CDs, so from the given information, $A+6=B-6$.

From the first equation, $B=2 A-18$; from the second equation, $B=A+12$.

Therefore, $2 A-18=A+12$ or $A=30$, and so $B=A+12=42$.

Thus, the total number of CDs that Ben and Anna have is $30+42=72$.

## Solution 2

Let $A$ be the number of CDs that Anna has.

If Anna receives $6 \mathrm{CDs}$ from Ben, then the two of them would have the same number of CDs. This tells us that Ben has 12 more CDs than Anne, or that Ben has $A+12$ CDs.

If Anna gives $6 \mathrm{CDs}$ to Ben, then Anna would have $A-6 \mathrm{CDs}$ and Ben would have $A+18$ CDs.

From the given information, $A+18=2(A-6)$ or $A+18=2 A-12$ or $A=30$.

Therefore, Anna has $30 \mathrm{CDs}$ and Ben has $30+12=42 \mathrm{CDs}$, so they have $30+42=72 \mathrm{CDs}$ in total.

ANSWER: (C)

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