Question

Sameer has a bag full of marbles he takes out half of the marble present in the bag and put back one marble in the bag he repeats it 4 times in the end only 3 marble are left in the bag how many marbles were there originally

Answer 1

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.

Answer 2

Find X:

Step 1: Total number of marbles in the bag = (x/2) +1,

Step 2: 1/2 (x/2 +1) +1 => x/4 + 3/2,

Step 3: (1/2) (x/4+3/2) + 1=> x/8 + 3/4 + 1 => x/8 + 7/4, Step 4: (1/2) (x/8 + 7/4) + 1=>  x/16 + 15/8.

Then solve X: x/16 + 15/8 = 3, multiply by 16 on both side ( x/16 + 15/8) 16 = 3 * 16 => x + 30 = 48 => x =18