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 Math Central Quandaries & Queries
 Question from Patti: A copy machine accepts nickels, dimes, and quarters. After 1 hour, there are 30 coins total, and their value is $\$5.10.$How many nickels, quarters, and dimes are in the machine? (Hint: There are exactly five different solutions.) Hi Patti: I can show you one approach. You could make the$\$5.10$ entirely in nickels but that would be 110 coins, far too many. Maybe it's better to start by maximizing the number of quarters rather than nickels.

You can make $\$5.00$with 20 quarters and then the remaining$\$0.10$ with one dime or two nickels but in either case it is too few coins. To increase the number of coins trade in one quarter for 2 dimes and 1 nickel. Thus you have made $\$5.00$with 22 coins. If you convert the 2 dimes to 4 nickels and make the remaining$\$0.10$ out of nickels but that is still too few coins.

Next I would try 18 quarters.

I hope this helps,
Penny