Question

Sam has a bag full of marbles.
He takes out half of the marbles present in the bag and puts back one marble into the bag. He repeats this process four times. In the end only three marbles are left in the bag.
How many marbles were there in the bag original

Answer 1

start with x marbles
step 1: marbles in bag = x/2 + 1
step 2: marbles in bag = (1/2)(x/2) + 1) + 1
= x/4 + 3/2
step 3: marbles in bag = (1/2)(x/4+3/2) + 1
= x/8 + 3/4 + 1 = x/8 + 7/4
step 4: marbles in bag = (1/2)(x/8 + 7/4) + 1
= x/16 + 7/8 + 1
= x/16 + 15/8

x/16 + 15/8 = 3
multiply by 16
x + 30 = 48
x =18