Question 1092998
The amount of many Jim put in his Piggy bank each day, in cents, is
{{{1+10+25=36}}}
After {{{n}}} days, with {{{n}}} being a positive integer, 
Jim had {{{36n}}} cents in his piggy bank,
and that was exactly {{{d}}} dollars, with {{{d}}} being a positive integer.
Those {{{d}}} dollars were exactly {{{100d}}} cents.
At that point it was true that {{{36n=100d}}} .
If we factor the numbers we know, we can write that equation as
{{{4*9*n=4*25*d}}} ---> {{{9*n=25*d}}} .
As {{{9}}} and {{{25}}} have no common factors other than {{{1}}} ,
and {{{n}}} and {{{d}}} are positive integers,
{{{n}}} must be a multiple of {{{25}}} ,
and the first time that could happen it would be after {{{n=highlight(25)}}} days.
At that point, Jim's piggy bank would have held
{{{4*9*25cents=900cents=highlight(9dollars)}}} .