find the 5 diff. ways a collection of 100 coins-pennies, dimes, and quarters- can be worth exactly worth $4.99.
$\displaystyle p+d+q=100$ and $\displaystyle p+10d+25q = 499$.
Thus, $\displaystyle 9d + 24q = 399$.
What are the possibilities for $\displaystyle d,q$ then?