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# Upon winning the lottery, John spent 13 of his winnings on a home and

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
Upon winning the lottery, John spent 13 of his winnings on a home and  [#permalink]

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23 Jan 2019, 00:49
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Difficulty:

45% (medium)

Question Stats:

54% (01:49) correct 46% (01:26) wrong based on 40 sessions

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Upon winning the lottery, John spent 1/3 of his winnings on a home and 1/4 of the remaining amount on a car. After these purchases, he had \$200,000 left. How much money did John win in the lottery?

A 400,000

B 480,000

C 600,000

D 800,000

E 2,400,000

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Re: Upon winning the lottery, John spent 13 of his winnings on a home and  [#permalink]

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23 Jan 2019, 01:23
Bunuel wrote:
Upon winning the lottery, John spent 1/3 of his winnings on a home and 1/4 of the remaining amount on a car. After these purchases, he had \$200,000 left. How much money did John win in the lottery?

A 400,000

B 480,000

C 600,000

D 800,000

E 2,400,000

lottery amount = x

cost of home = x/3

remaining = 2x/3

cost of car = 2x/3 * 1/4 = x/6.

remaining = 2x/3 - x/6 = 3x/6.

3x/6 = 200000

x= 400000.

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Re: Upon winning the lottery, John spent 13 of his winnings on a home and  [#permalink]

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23 Jan 2019, 05:20
Bunuel wrote:
Upon winning the lottery, John spent 1/3 of his winnings on a home and 1/4 of the remaining amount on a car. After these purchases, he had \$200,000 left. How much money did John win in the lottery?

A 400,000

B 480,000

C 600,000

D 800,000

E 2,400,000

x be total amount
eqn
x/3 + x/6 = 2* 10^5

x= 4* 10^5
IMOA
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Re: Upon winning the lottery, John spent 13 of his winnings on a home and  [#permalink]

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27 Jan 2019, 11:04
Bunuel wrote:
Upon winning the lottery, John spent 1/3 of his winnings on a home and 1/4 of the remaining amount on a car. After these purchases, he had \$200,000 left. How much money did John win in the lottery?

A 400,000

B 480,000

C 600,000

D 800,000

E 2,400,000

We can let n = the amount of money he won and create the equation:

n/3 + (1/4)(n - n/3) + 200,000 = n

n/3 - (1/4)(2n/3) + 200,000 = n

Multiplying the entire by 12, we have:

4n + 2n + 2,400,000 = 12n

2,400,000 = 6n

400,000 = n

Alternate Solution:

After spending 1/3 of the money, he is left with 2/3 of the prize and after spending 1/4 of this amount, he is left with 2/3 x 3/4 = 2/4 = 1/2; i.e. half of the prize money. If the remaining amount of 200,000 is half of what he had to begin with, then he won 200,000 x 2 = \$400,000.

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Re: Upon winning the lottery, John spent 13 of his winnings on a home and   [#permalink] 27 Jan 2019, 11:04
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