Question 175576
At the 1st store, he spent 
{{{x/2 + 1}}}
So, what he had left to spend was
{{{x - x/2 - 1}}}
{{{x/2 - 1}}}
At the 2nd store
He spent half this plus a dollar
{{{x/4 - 1/2 + 1}}}
{{{x/4 + 1/2}}}
So, what he had left to spend was
{{{x/2 - 1 - x/4 - 1/2}}}
{{{x/4 - 3/2}}}
At the 3rd store
He spent half of this plus a dollar
{{{x/8 - 3/4 + 1}}}
{{{x/8 + 1/4}}}
So, what he had left to spend was
{{{x/4 - 3/2 - x/8 - 1/4}}}
{{{x/8 - 7/4}}}
At the 4th store
He spent half of this plus a dollar
{{{x/16 - 7/8 + 1}}}
{{{x/16 + 1/8}}}
So, what he had left to spend was
{{{x/8 - 7/4 - x/16 - 1/8}}}
{{{x/16 - 15/8}}}
At the 5th store
He spent half of this plus a dollar
{{{x/32 - 15/16 + 1}}}
{{{x/32 + 1/16}}}
So, what he had left to spend was
{{{x/16 - 15/8 - x/32 - 1/16}}}
{{{x/32 - 31/16}}}
But, the problem says he spent all his money and
had nothing left, so
{{{x/32 - 31/16 = 0}}}
{{{x/32 = 31/16}}}
{{{x = (32*31)/16}}}
{{{x = 62}}}
He originally had $62
Now I can check the answer
At the 1st store, he spent 
{{{62/2 + 1}}}
{{{32}}}
So, what he had left to spend was
{{{62 - 32}}}
{{{30}}}
At the 2nd store
He spent half this plus a dollar
{{{30/2 + 1}}}
{{{16}}}
So, what he had left to spend was
{{{30 - 16}}}
{{{14}}}
At the 3rd store
He spent half of this plus a dollar
{{{14/2 + 1}}}
{{{8}}}
So, what he had left to spend was
{{{14 - 8}}}
{{{6}}}
At the 4th store
He spent half of this plus a dollar
{{{6/2 + 1}}}
{{{4}}}
So, what he had left to spend was
{{{6 - 4}}}
{{{2}}}
At the 5th store
He spent half of this plus a dollar
{{{2/2 + 1}}}
{{{2}}}
So, what he had left to spend was
{{{2 - 2}}}
{{{0}}}
OK
By the way, were you applying for a job as
a nuclear physicist?