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?

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