Question

The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?

Answer 1

Answer:

34 is the number

let the unit digit be x, then tens digiti be y

so the original number is 10y + x

where x+y = 7

the number reversed will be 10x + y

new number - old number = 9

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

9x - 9y = 9

x+y=7

x-y=1

add them

2x = 8

x = 4, then y = 3

the number is 10y+x = 34

HOPE IT HELPS

GOODNIGHT

Answer 2

Let the ten's digit and the one's digit be x and y respectively.

Given

The sum of the digits of a certain two-digit number is 7.

$\implies x+y=7--(1)$

Reversing its digits increases the number by 9.

$\implies 10y+x=10x+y+9\\\implies -10x+x+10y-y=9\\\implies -9x+9y=9\\\implies -x+y=1--(2)$

Solving (1) and (2), we get,

$x+y=7\\\underline{-x+y=1}\\\underline{\underline{2y=8}}\\\implies y = 4\\\implies x = 3$

$\boxed{\boxed{\bold{Therefore, \ the \ required \ number \ is \ 34}}}}}}}}$