A popular word problem using a system of equations is using coins.
Let’s say Jack has a piggy-bank in which, during the year, he fills with just pennies, nickels and dimes. As Christmas approaches, he empties the piggy-bank and counts the number of coins n. Then he totals their value $p. When he removes the pennies, the value goes down to $q. How many coins of each denomination are there?
(n, p and q will be actual numbers, for example, n=102, p=$3.84, q=$3.30.)