A collection of 39 coins consist of dimes and nickels. The total value is $2.85. How many dimes and how many nickels are there?

If all were dimes, the value would be 39*.10 = 3.90. It is 1.05 less than that. Each nickel that replaces a dime reduces the value by. 05, so there must be

... 1.05/.05 = 21 nickels

and 39-21 = 18 dimes