A Lucky Find
Outline Mathematics
Word Problems
Here's a problem to tackle:
A girl has lost $2. The girl's father remarked that had she found $2, she would have 5 times as much as she has now after the loss. How much money did the girl have, to start with?
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Solution
A girl has lost $2. The girl's father remarked that had she found $2, she would have 5 times as much as she has now after the loss. How much money did the girl have, to start with?
Assume the girl had m dollars. After she lost $2, she was left with only m  2,2m,2,m,m + 2,m  2 dollars. If she found $2, she would have m + 2,2m,2,m,m + 2,m  2 dollars. As the father has observed, the latter amount is 5 times as big as the former. In other words,
m + 2 = 5(m  2),m + 2 = 5(m  2),m + 5 = 2m,5(m + 2) = m  2.
Multiplying out gives: m + 2 = 5m  10,m  10 = 2m,m + 2 = 5m  10,m  2 = 10m  5, which simplifies to
4m = 12,6m = 12,4m = 8,4m = 12.
The solution then is m = 3,2,3,4,6 dollars.
Do not forget to check your solution.
References
 J. A. H. Hunter, Mathematical BrainTeasers, Dover Publications, 1976
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