Tim 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 more times. In the end, only three marbles are left in the bag.

Question

How many marbles were there in the bag originally?

Answer 1

working backwards,
x/2 + 1 = 3, so x=4
x/2 + 1 = 4, so x=6
now finish it off in two more steps

Answer 2

hi oobleck please help me on my work

Answer 3

english folktales

Answer 4

Define x:

Let the number of marbles in the bag be x

Take out half and put back 1 (1st Time):

⇒1/2 x + 1

Take out half and put back 1 (2nd Time):

⇒ 1/2 (1/2 x + 1) + 1

⇒ 1/4x + 1/2 + 1

⇒ 1/4x + 3/2

Take out half and put back 1 (3rd Time):

⇒ 1/2 (1/4x + 3/2) + 1

⇒ 1/8x + 3/4 + 1

⇒ 1/8 x + 7/4

Take out half and put back 1 (4th Time):

⇒ 1/2 (1/8 x + 7/4) + 1

⇒ 1/16 x + 7/8 + 1

⇒ 1/16 x + 15/8

Solve x:

There were 3 marbles left

1/16 x + 15/8 = 3

1/16 x = 3 - 15/8

1/16 x = 9/8

x = 9/8 ÷ 1/16

x = 18

Answer: There were 18 marbles in the bag.