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David inherited some money from his uncle. He invested half of the money with Bernie

Madoff (none of which he recovered), lost one-third of it due to identity theft, lost another

eighth of the money at a casino, and used the remaining $40,000 to buy a car.

How much money did David inherit?

Verified Answer :

meerkat18

Given:
Let x be the whole amount inherited.
1/2 x - invested with Bernie Madoff
1/3 x - lost due to identity theft
1/8 x - lost in casino
40,000 - remainder

x - x/2 - x/3 - x/8 = 40,000

LCM: 
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24, 

   x 24/24 = 24x / 24
x/2 12/12 = 12x / 24
x/3   8/8   = 8x / 24
x/8   3/3   = 3x / 24
40,000 24/24 = 960,000 / 24

24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 x/24 = 24 960,000/24
x = 960,000

x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.

960k - 480k - 320k - 120k = 40k
40k = 40k
 

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