SOLUTION: If we place a 3 at both ends of a number, its value is increased by 3372. Find the original number.

Algebra ->  Real-numbers -> SOLUTION: If we place a 3 at both ends of a number, its value is increased by 3372. Find the original number.      Log On


   

Question 1203099: If we place a 3 at both ends of a number, its value is increased by 3372. Find the original number.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If we place a 3 at both ends of an highlight%28integer%29 number, its value is increased by 3372.
Find the original number.
~~~~~~~~~~~~~~~~~~ 

Let the original integer number be x.

It is almost obvious (and easy to show) that the original number is a two-digit number.

If we place a 3 at both ends of such a number, its value becomes  3000+10x+3.


Therefore, according to the condition, we should find x from this equation

    (3000 + 10x + 3) - x = 3372.


It is easy

    10x - x = 3372 - 3000 - 3

       9x  = 369

         x  =  369/9 = 41.


CHECK.  3413 - 41 = 3372, the increase value.   ! correct !


ANSWER.  The original number is 41.

Solved.