I need help on understanding and do a reverse digit problem.

problem is:

If you take two-digit number to make a second two-digit number, and add these numbers together, their sun will be 121. What is the original number??

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- Aug 18th 2009, 03:25 PMYaquiShamanReverse Digit problem help
I need help on understanding and do a reverse digit problem.

problem is:

If you take two-digit number to make a second two-digit number, and add these numbers together, their sun will be 121. What is the original number?? - Aug 18th 2009, 03:38 PMBruno J.
First number is $\displaystyle 10a+b$

Reverse the digits, you get $\displaystyle 10b+a$

add the two to get $\displaystyle 10(a+b)+(a+b)=11(a+b)=121$

so you must have $\displaystyle a+b=11$. Possible choices (up to reversing the digits) are $\displaystyle 29,38,47,56$. - Aug 18th 2009, 03:46 PMYaquiShaman
Thanks for the answer and i understand how to do the problem now.

- Aug 18th 2009, 03:48 PMBingk
I'm assuming that when you say you "take two-digit number to make a second two-digit number", you make the second number by reversing the digits.

Let*x*be the first digit, and*y*be the second digit.

Your first number is*x*+ 10*y*, so your second number is 10*x*+*y*

When you add the two numbers together you have

(*x*+ 10*y*) + (10*x*+*y*) = 10*x*+*x*+ 10*y*+*y*= 11*x*+ 11*y*= 11(*x*+*y*) = 121

So*x*+*y*= 11

Remember,*x*and*y*represent the digits, so they are single digit numbers.

So, we have:

x y

2 9

3 8

4 7

5 6

6 5

7 4

8 3

9 2

i.e. 29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 65 + 56 = 74 + 47 = 83 + 38 = 92 + 29 = 121