In each store Johnny spent $1.00 more than half of what he had when he came in. How much money did he get from grandma?

Question

Grandma sent Johnny some money for his birthday. Johnny spent all of it in five stores. In each store, he spent $1.00 more than half of what he had when he came in. How much money did he get from grandma?

Answer 1

Ans is $62
62/2=31+1=32,bal=62-32=30.......Store(1)
30/2=15+1=16,bal=30-16=14.......Store(2)
14/2=07+1=08,bal=14-08=06.......Store(3)
06/2=03+1=04,bal=06-04=02.......Store(4)
02/2=01+1=02,bal=02-02=00.......Store(5)
Johnny gets $62 from grandma

Answer 2

let the amount given by grandma=x
As he spends half of his previous amount +1 in each store.
In first store, he spent x/2+1=(x+2)/2
money left with johnny after visiting first store x-((x+2)/2)=(x-2)/2
In 2nd store ,(x-2)/4+1=(x+2)/4
money left with him after visiting 2nd store=(x-2)/2-(x+2)/4=(x-6)/4
3rd store=(x-6)/8+1=(x+2)/8
left money after visiting 3rd store=(x-6)/4-(x+2)/8=(x-14)/8

in 4th store, (x-14)/16+1=(x+2)/16
money left after visiting 4th store=(x-14)/8-(x+2)/16=(x-30)/16

In 5th store, (x-30)/32+1=(x+2)/32
money left with him after visiting fifth store=(x-30)/16-(x+2)/32=(x-62)/32

He spent all his money so he left with zero amount after visiting all store=
At last he had money =0
(x-62)/32=0
x-62=0
x=62
so , grandma gave him=$62