Responses/hints:

As with many of the puzzles we use, this puzzle has more than one solution. That is, there is more than one way to work through the given and find a solution.

Here are two ways to approach this puzzle:

Let P stand for the number of pennies, N the number of nickels, and D the number of dimes below.

You could think of the number of pennies in terms of the nickels: P = 7-N, and the number of dimes in terms of nickels: D = 5-N.

Then the 9 coins would have to equal 7-N + N + 5-N = 9, so you can find the number of nickels, and then work back through the given to find the number of each coin?

Another approach is to write out each of the 3 given statements in terms of equations and the unknowns P, N, & D:

P + N + D = 9

P + N = 7

N + D = 5

and then solve this system for P, N, & D.

Maybe you found another way of reasoning through this Puzzle? If so, please drop me a line and give your argument. I would like to see it!