August 2012
Problem of the Month

Hardware Problem

Lou bought a switch plate, a can of glue, and a spool of solder at the hardware store.

All together, they cost exactly $15.00.

Each item's price contained the same three digits in a different order.

None of the digits in the prices were zeros, and the solder cost $4.50 more than the switch plate.

How much did the glue cost?

Solution to the Problem:

The glue cost $7.16.

Let ABX = cost of the solder
Then BAX = cost of the switch

So, ABX - BAX = 450

Using algebra,
(100A + 10B + X) - (100B + 10A + X) = 450

So, 90A - 90B = 450 or

A - B = 5

There are only 4 possibilities for A and B:

A = 6, B = 1;       A = 7, B = 2;
A = 8, B = 3;       A = 9, B = 4;      

If A = 6 and B = 1, then the third digit must be 7 in order to add up to 15:
      6.17
      1.67
      7.??
      ----
     15.00

In order to add up to $15.00, the glue must cost $7.16.

Correctly solved by:

1. Mary Murtishaw	Cabot, Arkansas
2. James Alarie	Flint, Michigan

Send any comments or questions to: David Pleacher