Question

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.

Answer 1

57 and 75.

Answer 2

I can't choose both.

Answer 3

& how did you find the answer ?

Answer 4

The original number is 75

Answer 5

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

Answer 6

75 i think?

Answer 7

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.