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## How to setup an equation for this...

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seal4913 Really wants to Beat The GMAT!
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How to setup an equation for this... Sat Apr 14, 2012 9:58 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
I solved the following by just plugging in but what would be the way to solve creating an equation?

A man wins the lottery and gives half of the prize money to his wife, one third of the remaining money to his son and then half of what is left to his daughter. If his daughter received \$2000, how much was the original prize?

A) \$6,000
B) \$9,000
C) \$12,000
D) \$18,000
E) \$24,000

As suggested I start with C. So if I have 12k and give half away I have 6k. I give 1/3 away so 1/3 of 6k is 2k so I'm left with 4k and then I give half of what's left so that's 2k. 4k - 2k is 2k and that fits. Therefore it's C.

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seal4913 Really wants to Beat The GMAT!
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Sat Apr 14, 2012 10:08 am
I think I got it...

y = .5A; z = y - 1/3y ; x = z - .5z;

So x equals 2000; 2000 - .5z therefore z = 4000. So 4000 = 2/3y which equals 6000; so 6000 = .5A and A = 12000

Birottam Dutta GMAT Destroyer!
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Sat Apr 14, 2012 11:43 am
Let A be the amount won in the lottery.

Amount given to wife = 1/2A

Amount left = 1/2 A

Amount given to son= 1/3 * 1/2 A

Amount left = 1/2A-(1/3*1/2A) = 2/3*1/2A

Amount given to daughter = 1/2 * (2/3*1/2A)

By, the statement, amount given to daughter = \$2000 => 1/2*2/3*1/2A= \$2000 => A= 12000

Hence, C

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