During hibernation, a bear loses $20 \%$ of its original mass. After hibernation, its mass is $220 \mathrm{~kg}$. What was its mass, in kilograms, just before hibernation?
(A) 176
(B) 264
(C) 240
(D) 275
(E) 1100
Solution 1

Since the bear has lost $20 \%$ of its original mass, then the $220 \mathrm{~kg}$ represents $80 \%$ of its original mass. Therefore, $20 \%$ of its original mass is $55 \mathrm{~kg}$ (one quarter of $220 \mathrm{~kg}$ ), and so its mass before hibernation was $220+55=275 \mathrm{~kg}$. (Notice that this just amounts to

$\frac{5}{4} \times 220=275$.)

## Solution 2

Let $x$ be the bear's mass just prior to hibernation.

Since the bear loses $20 \%$ of its mass during hibernation, then

$$
\begin{aligned}
\frac{80}{100} x & =220 \\
x & =\frac{100}{80}(220) \\
x & =275
\end{aligned}
$$

Therefore, the bear's mass just before hibernation was $275 \mathrm{~kg}$.

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