   SEARCH HOME Math Central Quandaries & Queries  Question from Ana, a student: you have 50 coins which have a total value of 1.00. What are the coins and how many of each do you have? Ana,

What are the coins and how many of each do you have?

In principle problems like this can be approached using generating functions; unless you know what this means I'm going to assume more primitive methods.

Think about what you can say about the number of cents. Of your 50 coins how many must be cents if the total is not to be over 1.00?

Could you have exactly 43 cents? Why or why not? What additioanl conclusions can you draw?

You should now have a rather short list of possible numbers of cents. In turn, assume each of these, and subtract them form both the coin count and the total. Thus for 45 cents your new problem would be:

"You have 5 coins, all bigger than a cent, which have a total value of \$0.55"

Use similar methods on this simpler problem. You can also start "at the large end" by considering possible numbers of quarters. There may be no solutions, or multiple solutions. If there are multiple solutions you should try to find them all.

Good hunting!

RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.