There is a two digit number with the unique property that if a decimal point is inserted between the two digits, the resulting number is the average of the digits. What is the number?

The number is 45.  The sum of the two digits is 9 (= 4 + 5), with the average being 4.5 (= 9 / 2).

We know the number is only two digits with the total of the two digits when added to be halved to get the average, thus we know the number must end in a 5.

Given that n is the tens-digit of the number, an equation can be written as n + 5 = 2*(n + .5).  Solving mathematically, n = 4.  Thus the number is 45. 

Edited on May 4, 2007, 2:19 pm

Posted by Dej Mar on 2007-05-04 14:08:35