# 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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Copyright © 1996-2018 Alexander Bogomolny

### 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 Brain-Teasers*, Dover Publications, 1976

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Copyright © 1996-2018 Alexander Bogomolny