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 zeroes, 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 |