Robbery

[chieftang]

A thief stole 3/5 of Genevieve's money and spent 3/5 of the money stolen. The thief was then caught, and the remaining money was returned to Genevieve. The remaining money was 40 dollars less than the amount Genevieve had after being robbed. How many dollars did Genevieve have before the theft?

A. 200
B. 225
C. 250
D. 260
E. 275


Source: MATHCOUNTS problem bank.

[Anurag@Gurome]

A thief stole 3/5 of Genevieve's money and spent 3/5 of the money stolen. The thief was then caught, and the remaining money was returned to Genevieve. The remaining money was 40 dollars less than the amount Genevieve had after being robbed. How many dollars did Genevieve have before the theft?

A. 200
B. 225
C. 250
D. 260
E. 275

Source: MATHCOUNTS problem bank.

Let us assume that Genevieve had $x before the theft.
Thief stole = 3x/5
Amount left with Genevieve = x - 3x/5 = 2x/5
Amount spent by thief = (3/5)(3x/5) = 9x/25
Money left with thief = 3x/5 - 9x/25 = 6x/25, which was returned to Genevieve.
6x/25 = 2x/5 - 40
40 = 4x/25 or x = [spoiler]$250[/spoiler]

The correct answer is C.