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Adam and Ben shared a sum of $600. Adam gave 1/4 of his money to Ben. After that, Ben gave 1/3 of his money to Adam. In the end, Ben had 3/2 as much money as Adam. How much money did Adam have at first?

 Dec 31, 2023
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At first, Adam had A dollars and  Ben had 600 - A dollars

B = 600 - A

 

After  Adam gave (1/4) of his  money to  Ben

 

Adam had  (3/4)A

Ben had   600 - A + (1/4) A  =  600 - (3/4)A

 

After Ben gave (1/3)  of his  money to Adam

 

Adam had  (3/4)A +  [ 600 - (3/4)A ] / 3  =    200 + (1/2)A

Ben had   (2/3) [ 600 - (3/4)A ]  =  400 - (1/2)A

 

And in the end  Ben had (3/2)as much as Adam

 

400 - (1/2)A  =  (3/2) (200 + (1/2)A )

 

400 - (1/2)A  =  300 + (3/4)A

 

100 =  (5/4)A

 

100 (4/5) =  A  =  $80   (Adam  started with $80 )

 

Proof :

 

At first   :   A = 80      B =  520

 

After the first transaction :     A = 60      B =  540

 

After the second transacyion :   A = 240  B = 360   ⇒   B/ A = 360 / 240  = 3 / 2

 

 

cool cool cool

 Jan 1, 2024

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