Question

Alan had some cards and he gave some to two friends, Ben and Carl.
Alan first gave 1/3 of his cards and 8 more cards to Ben.
Alan then gave 3/4 of the remainder to Carl and 2 more cards.
In the end, Alan was left with 46 cards. How many cards did Alan have at first?

Thanks for your help.

Answer 1

ben got 1/3 x + 8, leaving 2/3 x - 8
carl got 3/4 (2/3 x - 8) + 2
so, doing the math,
x - (1/3 x + 8) - 3/4 (2/3 x - 8) = 46
Now solve for x

Answer 2

200