Question 126836
$5.00 is 500 cents, 10d is the amount in cents received from selling d items for a dime, and 25q is the amount in cents received from selling q items for a quarter.


{{{10d + 25q < 500}}}


This could also be expressed as {{{0.10d + 0.25q=5.00}}}, but I happen to think decimal coefficients are messy and best avoided if possible.  Then again, maybe I'm related to Monk.


The maximum number of items that could have been sold for a dime is when zero items sold for a quarter, so the inequality reduces to:


{{{10d < 500}}}


Dividing by 10:
{{{d < 50}}}


Since fractional parts of a dime are not allowed in this situation, the most items that could have been sold for a dime was 49, one less than 50.