amount originated

Question

if a man spends one fifth of what is in his wallet and then one fifth of what remained, and has spent $72.00, what was the amount originally in his wallet?

 

Answer 1

Sorry Robert & Vivian for calling y'all out, but I think y'all have erred.

 

The man originally had $200 in his wallet.

 

He spent 1/5 of what was in his wallet, which is $40.  Then $160 remains.  Then if he spends 1/5 of what remains, that's $32.  Thus he's spent a total of $40+$32 = $72.

 

***

 

1)  One way of solving this is to first say that "x" represents the total originally in the man's wallet.

 

2)  If he spends 1/5 of what's in his wallet, he's spent (1/5)x, and that means that there's still (4/5)x in his wallet.

 

3)  Then if he also spends 1/5 of what remains, he spends an additional (1/5)*(4/5)x.

 

4)  The total he's spent thus far, then, is given by (1/5)x + (1/5)*(4/5)x.  The problem tells us that equals $72, so we can solve:

 

(1/5)x + (1/5)*(4/5)x = 72

 

(1/5)x + (4/25)x = 72

 

(5/25)x + (4/25)x = 72

 

(9/25)x = 72

 

x = 72 * (25/9) = 8 * 25 = 200.

 

So he originally had $200 in the wallet.

 

Answer 2

Hello Me -- another angle: the 2nd outlay must be 4/5ths of the 1st outlay "x" ...

 

1.8x = $72 ... 72 over 1.8 ... scale up by 2/3rds ... 120 over 3 ... x= $40 ...

 

since the 1st outlay of $40 is 1/5th of original wallet ==> $200 to start ... Regards :)

Answer 3

Hi Me;

Sorry, Me.  After Murtaza's correction, I decided it was time to go to sleep.

x=original amount

He spent (1/5)th of x. Then, (4/5)ths remained and he spent (1/5)th of that.

[(1/5)(x)]+[(1/5)(4/5)x]=$72.00

[(1/5)x]+[(4/25)x]=$72.00

[(5/25)x]+[(4/25)x]=$72.00

(9/25)x=$72.00

Let's multiply both sides by (25/9)...

(9/25)(25/9)x=$72.00(25/9)

x=$200.00

 

Answer 4

Let x be the original amount.

Balance by spending,

x - (4/5)^2 x = 72, focusing on the remaining part each time.

Solve for x,

x = $200

Answer: The original amount was $200.

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Hi Murtaza;

You are correct. I misread the problem. This problem can be done as above.