April 2015
Problem of the Month

The Wheel Thing
by Raymond Love
GAMES April 2015

Wheeler's Toy Store has a number of bicycles, tricycles, and wagons in stock.

If there are an equal number of tricycles and wagons, and a total number of 60 pedals and 180 wheels, how many wagons, tricycles, amd bikes are there in in the store?

Solution to the Problem:

There are 24 wagons, 24 tricycles, and 6 bikes.

Let t = # of tricycles
Let b = # of bikes
Let w = # of wagons

Then we can write the following three equations:
t = w
2(b + t) = 60
4w + 2b + 3t = 180

Solving, we get:
b + t = 30
2b + 7t = 180 (substituting w = t in the third equation above)
So, 5t = 120 and t = 24
Then it follows that w = 24 and b = 6.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Brooks Garris	Lake View High School, Lake View, South Carolina
3. Braydon Saxton	Mountain View High School, Mountain View, Wyoming
4. Chad Fore	Gate City, Virginia
5. Chana B.	New York
6. Keith Mealy	Cincinnati, Ohio
7. Michael Reilly	Silver Spring, Maryland

Send any comments or questions to: David Pleacher