## anonymous 4 years ago The sum of the digits of a two-digit number is 12. When the digits are reversed, the new number is 18 less than the original number. Find the original number.

1. Hero

57 and 75.

2. anonymous

I can't choose both.

3. anonymous

& how did you find the answer ?

4. Hero

The original number is 75

5. Hero

That's a good question. I used trial and error, but there should be a way to solve this algebraically.

6. anonymous

75 i think?

7. KingGeorge

If you want to solve it algebraically, simply use two variables x1, and x2 such that x1 represents the tens place, and x2 the ones place. Then, we can make the equations$\begin{matrix}x_1 +x_2=12 \\ 10x_1 + x_2 = 10x_2 + x_1 +18 \end{matrix}$ Then, using simple algebra, this can be solved for $\begin{matrix} x_1 = 7 \\x_2 = 5 \end{matrix}$ Giving us the original number: 75.