SOLUTION: a 2 digit number is 3 times the sum of its digits. The number is also less 45 less than the number formed by reversing the digits original number. What is the original number?

Question 919516: a 2 digit number is 3 times the sum of its digits. The number is also less 45 less than the number formed by reversing the digits original number. What is the original number?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Let the tens digit be t and the units digit be u.  Then the number
is 10t+u.

a 2 digit number

10t+u

equals

3 times the sum of its digits.

 3(t+u)

So that says

10t+u = 3(t+u)

10t+u = 3t+3u

   7t = 2u

   

So the only way that can be is t=2 and u=7

The number is also less 45 less than the number formed by reversing the digits original number.

Let's see.  If we reverse 27 we get 72 and 72-27 = 45, so yes that is true of 27.

What is the original number?

27

Edwin

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