Find odd number with three digits. All digits are different and add up to 12. Difference between 1st two digits = difference between last two digits.

Expert Answers

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Let the three digit number be abc

Given that the sum of the digit is 12

==> a + b + c = 12..........(1)

Also, given the difference between the first two digit = the difference between the last two digits:

==> l a-b l = l b-cl

==> (a-b) = (b-c)

==> (a+c) = 2b

Now we will substitue in (1)

==> a+ b + c = 12

==> 2b + b = 12

==> 3b = 12

Now divide by 3:

==> b = 4

==> a+c = 2b= 8

==> a = 8-c ..........(2)

We know that"

(a-b) = (b-c)

==> a > b+c

==> a > 4 + c

==> 8-c > 4+c

==>4 > 2c

==> 2 > c

Since c is an odd integer, then c must be 1

==> b= 4  c = 1  ==> a =  7

Then the three digit number is 741

Approved by eNotes Editorial Team
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