+77 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?
+128731 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
