During 1996, the population of Sudbury decreased by $6 \%$ while the population of Victoria increased by $14 \%$. At the end of the 1996, the populations of these cities were equal. What was the ratio of the population of Sudbury to the population of Victoria at the beginning of 1996?
(A) $47: 57$
(B) $57: 47$
(C) $53: 43$
(D) $53: 57$
(E) 43:47
Solution

Let $s$ represent the population of Sudbury at the beginning of 1996, and $v$ represent the population of Victoria at the beginning of 1996.

At the end of 1996, Sudbury's population was $0.94 s$ and Victoria's population was $1.14 v$, where $0.94 s=1.14 v$ (1).

To find $s: v$, rearrange (1) to obtain

$$
\frac{s}{v}=\frac{1.14}{0.94}=\frac{57}{47}
$$

ANSWER: (B)

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