Problem 1

 

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.