** **

A coin collection consists of nickels, dimes and quarters. There are 20 coins in the collection with a total value $2.00, and the number of nickels is three times more than the number of quarters.

Find __all__ possible solutions of the numbers of coins
of each kind.

[Problem submitted by Vick Vardanyan, LACC Instructor of Mathematics.]

**Solution for Problem 1:**

** **

Let n be the number of nickels, d be the number of dimes, q the number of quarters.

Then n+d+q=20 (1)

5n+10d+25q=200 (2)

n=3q (3)

Substituting (3) into (1) and (2) and simplifying one gets
the __same __equation: d+4q=20.

But the possible positive integer solutions are

q=1, d=16, n=3

q=2, d=12, n=6

q=3, d=8,
n=9

q=4, d=4, n=12.