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

Question

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

KSBGC · Answer

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.

A is the correct answer.

Archit3110 · Answer

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

x= 4* 10^5
IMOA

ScottTargetTestPrep · Answer

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.

Answer: A

hemantbafna · Answer

Let the amount he won be x

Home=1/3*x 
Car=1-x/3*1/4=2x/12=x/6

x-x/3-x/6=200000
3x/6=200000
x=400000
 A

MathRevolution · Answer

Let the lottery amount won by John was 120 ( Assume an initial value for simple calculation. Usually, it is better to assume 100, but in the question, as we have  \frac{1}{3}  and  \frac{1}{4} , take LCM of 3 and 4 that is 12 and assume the lottery amount to be 120)

John spent  \frac{1}{3}  of his winnings on a home :  \frac{1}{3}  *120 = 40 (spent) ---->  Remaining 120-40 = 80. 
John spent  \frac{1}{4}  of the remaining amount on a car:  \frac{1}{4}  * 80 = 20 (Spent) ----->  Remaining = 60. 
 
  Initial amount --------> Remaining amount 
 120 --------> 60
 ? --------> $200,000 (Given in the question)

? = 120 * 200,000 / 60 = $400,000

Answer A

Short Approach:

John total spending :  \frac{1}{3}  +  \frac{2}{12}  = \frac{6}{12}  =  \frac{1}{2} .  \frac{1}{3}  spending John is left with  \frac{2}{3}  of amount out of which he spends  \frac{1}{4}  that is  \frac{2}{3} * \frac{1}{4}  =   \frac{2}{12}

He is left with  \frac{1}{2}  which is $200,000.

Therefore,  \frac{1}{2}  * Total lottery amount = $200,000

Total lottery amount = $400,000

Answer A

Palak74 · Answer

3/4th of the 2/3 remaining is 200000
i.e 1/2 is 200000

Therefore, full amount will be 400000 
Option A

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

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