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11 Sep 2026, 12:10
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C
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During the year 2003, the number of unemployed people in Arkland increased by 1/4, whereas the number of unemployed people in Bonnyville increased by 1/6. The increase in the number of unemployed people in Bonnyville during the year was 1/10 greater than the increase in Arkland. At the end of 2003, the number of unemployed people in Bonnyville was what percent greater than the number of unemployed people in Arkland?
A. 25%
B. 35%
C. 54%
D. 65%
E. 75%
A. 25%
B. 35%
C. 54%
D. 65%
E. 75%
11 Sep 2026, 13:54
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kevincan
This deceptively tricky problem is a great illustration of the importance of careful interpretation.
If the number of unemployed people in Arkland (call it a) increased by 1/4, then the amount of the increase was \(\frac{1}{4}a\).
Likewise, Bonnyville's increase is \(\frac{1}{6}b\).
Bonnyville's increase was 1/10 greater than Arkland's, so:
\(\frac{1}{6}b=\frac{11}{10}(\frac{1}{4}a)\)
\(\frac{1}{6}b=\frac{11}{40}a\)
The question asks what percent greater is the number of unemployed in Bonnyville vs. Arkland at the end of 2003. In other words, you are not asked for the percentage difference between b and a, but the percent difference between \(\frac{7}{6}b\) and \(\frac{5}{4}a\).
We can represent this unknown difference as simply x (we will convert to a percentage later):
\(\frac{7}{6}b=x(\frac{5}{4}a)\)
Now we just need to substitute. One good way to do this is to multiply \(\frac{1}{6}b=\frac{11}{40}a\) by 7:
\(\frac{7}{6}b=\frac{77}{40}a\)
Then substitute:
\(\frac{77}{40}a=x(\frac{5}{4}a)\)
\(77=50x\)
\(x=\frac{77}{50}=\frac{154}{100}\)
Thus, at the end of 2003 the number of unemployed in Bonnyville is 154/100 of the number of unemployed in Arkland, or 54% more. The answer is C.
Note the trap answer D, 65%, which represents the percentage difference before the increase in 2003.
It's worth it to spend time up front understanding and interpreting the prompt rather than diving in to solve immediately. Similarly, before you confirm your answer make sure that you've answered the right question. This can save you from many common traps and misinterpretation errors.
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