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.

Let 10x+y be the original number

x+y=15

10x+y-27=10y+x

Solving the equation, we have x=9, y=6

Hence the number is 96

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