$1.00

I have only nickels, dimes, and quarters and have at least one of each type of coin. The total number of coins I have is fifteen and the total value of all the coins is $1.00. How many of each coin do I have?

Answer:

Thirteen nickels, one dime, and one quarter

The cleverest way to solve this problem is to try to reduce the number of possibilities to a minimum and then figure out all of those possibilities. The highest number of quarters I can have is three, since if I have at least one of every coin, I can't have four quarters (and I can't have more than four quarters because the total would be more than $1). So, if I have three quarters, I am left with fourteen dimes/nickels, which most add up to 25 cents. That's impossible, so suppose I have two quarters. That leaves 50 cents for the dimes/nickels. I can't get fourteen dimes/nickels that add up to 50 cents. So, try one quarter. I have 75 cents left. I can get thirteen nickels and one dime to total 75 cents.