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?

sugabreaddoughman Dec 31, 2023

#1**+1 **

At first, Adam had A dollars and Ben had 600 - A dollars

A

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

CPhill Jan 1, 2024