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?

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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?

posted Dec 12, 2015
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2 Answers

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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 Dec 12, 2015
0 votes

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

answer Dec 8, 2016

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