Question

The sum of the digits of a two-digit number is 9. Also, nine times this number is
twice the number obtained by reversing the order of the digits. Find the number.

by substitution method ​

Answer 1

Answer: 18

Step-by-step explanation:

Two digit number: 10x + y

x + y =9..........eqn. 1

From eqn. 1 we have,

y = 9 - x

Reversed order of digits = 10y + x

9(10x + y) = 2(10y + x)

90x + 9y = 20y + 2x

90x - 2x = 20y - 9y

88x = 11y.........eqn.2

Substitute (y= 9-x) in eqn. 2

88x = 11(9 - x)

88x = 99 - 11x

88x + 11x = 99

99x = 99

x = 99/99

= 1

Substitute value of x in eqn. 1

x + y =9

1 + y = 9

y = 8

Number = 10x + y

= 10(1) + 8

= 10 + 8

= 18