Zachary paid for a $\$1$ burger with 32 coins and received no change. Each coin was either a penny or a nickel. What was the number of nickels Zachary used?
I need to find the number of nickels, let's call it n, that Zachary used. If n is the number of nickels, then 32 - n is the number of pennies, since he used 32 coins in total. I also know that the total value of the coins must be $\$1$, or 100 cents. So I can write an equation that relates the value of the coins to the number of coins: 5n + 1(32 - n) = 100. This equation simplifies to 4n + 32 = 100, or 4n = 68. Dividing both sides by 4, I get n = 17. So Zachary used 17 nickels and 32 - 17 = 15 pennies. 