The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 less than the original number.

Find the number.

83.

Step-by-step explanation:

Let the digits be x and y so the number is xy.

x + y = 11

The new number is 45 less than the original number so

10y + x = 10x + y - 45

-9x + 9y = - 45

-x + y = - 5

x + y = 11 Adding:

2y = 6

y = 3

and x = 11/3 = 8.

So the number is 83.