Question

A number consist of 2 digits whose sum is 8, If 8 is subtracted from the number, the digits interchange their place. The number is​

Answer 1

`x+y=8\\10x+y-8=10y+x\\\\x+y=8|\cdot9\\9x-9y=8\\\\9x+9y=72\\\underline{9x-9y=8}\\18x=80\\x=(80)/(18)=(40)/(9)`

x is not integer, so there must be a mistake in the problem.

Answer 2

Explanation:

Let's say the two digit number is 10x + y, where x is the first digit and y is the second digit.

The sum of the digits is 8:

x + y = 8

If 8 is subtracted from the number, the digits switch place.

10x + y − 8 = 10y + x

Simplify the second equation:

9x − 8 = 9y

Substitute from the first equation.

y = 8 − x

9x − 8 = 9 (8 − x)

9x − 8 = 72 − 9x

18x = 80

x = 4.444

There's a problem. x isn't an integer. Are you sure you copied the problem correctly? Perhaps you meant if 18 is subtracted from the number, the digits switch place.

9x − 18 = 9 (8 − x)

9x − 18 = 72 − 9x

18x = 90

x = 5

y = 8 − x

y = 3

So the number is 53.