Derek had 104 more stamps than Ahmad. Derek then gave 1/9 of his stamps to Ahmad. In the end, Derek had 4 times as many stamps as Ahmad. How many stamps did Derek have at first?
Ahmad -- x
Derek --- x+104
after exchange:
Ahmad ---- x + (1/9)(x+104)
Derek ---- (8/9)(x+104)
(8/9)(x+104) = 4(x + (1/9)(x+104) )
(8/9)(x+104) = 4x + (4/9)(x+104)
times 9
8(x+104) = 36x + 4(x+104)
8x + 832 = 36x + 4x + 416
416 = 32x
x = 13
So, at the start, Ahmad has 13 and Derek had 117
check:
Derek gave (1/9)(117) or 13 to Ahmad,
so Derek now has 104
and Ahmad now has 26
Is 104 equal to 4 times 26 ??