## Problem of the Week:  Making Change at the Boutique Shop (Teacher Page)

In the Boutique Shop, you must determine the change a customer receives from \$5.00 for each purchase and decide what coins you use to make the change.  You have quarters, dimes, nickels, and pennies.* (Below is a list of 8 possibilities.)

*Limit: 9 of any one coin

• List all the different ways you can make change in this problem?
• What is the least number of coins you need to find this change? (6)
• Whats the most number of coins you can use to find this change if you have a limit of 9 of any particular coin? (18)
• Why can you use only 8 pennies or 3 pennies? (Why not 9, 7, 6, 5, 4, 2, 1, or 0?) Try some of the numbers in parenthesis and see what happens. For example, if you have 9 pennies, then you have to make \$.69 with the remaining coins. How do you make \$.69 with only quarters, dimes and nickels? The amount that you make with the combinations of these three coins has to be a multiple of 5. So if you subtract the number of pennies from your required change, then that number has to be a multiple of 5.