The different of the digits of a two-digit number is 7. The number is nine times the sum of its digits. Find the number.

Let x, y be the two digits.

The number is xy.

x-y=7.

10x+y=9(x+y).

from equation 1 x=y+7.

10(y+7)+y=9(y+7+y).

10y+70+y=18y+63.

11y+70-18y+63.

18y-11y=70-63.

7y=7.

y=1.

x=y+7 =1+7.=8.

The number is 81.