math word problem

Question

Sania was given some money by her father on her birthday. Sania spent all of it in five shops. In each shop, she spent one rupee more than half of what she had when she came in. How much did she get from her father?

Answer 1

Amount given by her father = x

STORE 1:

   start with x, spend x/2  + 1, leaves x/2  - 1

STORE 2:

   start with x/2 - 1, spend 1/2[x/2 -1] + 1, leaves x/4 - 3/2

STORE 3:

   start with x/4 - 3/2, spend 1/2[x/4 - 3/2] + 1, leaves x/8 - 7/4

STORE 4:

 start with x/8 - 7/4, spend 1/2[ x/8 - 7/4] + 1, leaves x/16 - 15/8

STORE 5:

 start with x/16 - 15/8, spend 1/2[x/16 - 15/8] + 1,

 leaves x/32 -31/16

If she has spent all of it, then x/32 - 31/16 = 0

 

So x/32 = 31/16, or x/32 = 62/32, so  x = 62 RUPEES