the sum of the digits of a two digit number is 15. if the digits are reversed, the new number is 27 less than the original number. find the original number.

Define original value of the two digit
I make an example, a is the first digit and b is the second digit. The original value of the digit will be
10a + b
because a stands as tens and b stands as units

Make an equation system
The sum of two digit is 15
⇒ a + b = 15 (this is first equation)
If the digits are reversed, the new number is 27 less than the original number. That means b will stand as tens, and a will stand as units.
⇒ 10b + a = (10a + b) - 27  (this is second equation)

Solve the equation
To find the numbers, we should solve the first and second equation.
From the first equation
a + b = 15
a = 15 - b

Subtitute 15 - b to a in the second equation
10b + a = 10a + b - 27
10b + (15 -b) = 10(15 - b) + b - 27
9b + 15 = 150 - 10b + b - 27
9b + 10b - b = 150 - 27 - 15
18b = 108
b = 6

Subtitute 6 as b to the first equation
a = 15 - b
a = 15 - 6
a = 9

The original number is 96