The sum of a particular two digit number is 5. If this numbers digits are reversed. The number is decreased by 9 what is the number?
Set up using system of equations

The number is 32

Solution:

The number is 10y + x (original)

Let the units place be x

Let the tens place be y

The sum of a particular two digit number is 5

Therefore,

x + y = 5 eqn 1

If this numbers digits are reversed, then the number is decreased by 9

numbers digits are reversed = 10x + y ( digits are reversed )

Then, the number is decreased by 9

10y + x - 9 = 10x + y

10y + x - 10x - y = 9

-9x + 9y = 9

Divide by 9 entire equation

-x + y = 1 eqn 2

Add eqn 1 and eqn 2

x + y - x + y = 5 + 1

2y = 6

y = 3

Substitute y = 3 in eqn 2

-x + 3 = 1

-x = 1 - 3

-x = -2

x = 2

Thus the original number is:

Number = 32