SOLUTION: the sum of the digits of a two digit number is 11. the new number obtained when the digits are reversed is 7 more than twice the original number. find the original number.(use only

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the sum of the digits of a two digit number is 11. the new number obtained when the digits are reversed is 7 more than twice the original number. find the original number.(use only      Log On


   

Question 1132112: the sum of the digits of a two digit number is 11. the new number obtained when the digits are reversed is 7 more than twice the original number. find the original number.(use only one variable and this is a digit number problem) (thanks in advance)
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let the ones digit of the number is A; then the tens digit is (11-A).

Hence, the digit itself is  10*(11-A) + A.


Then the digits are reversed in the number, the new number is  10A +(11-A).


The new number and the original number are related each to other by this equation


10A + (11-A) = 2*(10*(11-A) + A) + 7.


We just completed the setup.
We have now one equation for single unknown A.


Simplify and solve for A:


10A + 11 - A = 2*(110 - 10A + A) + 7

9A + 11 = 220 - 18A + 7

9A + 18A = 227 - 11

27A = 216

A = 216%2F27 = 8.


ANSWER.  The ones digit is  8.  The tens digit is  11-8 = 3.  The number itself is  38.

Solved.

Check it on your own that the solution and the answer are correct.

Good problem. Hope everything is clear to you.