How do you solve this problem?

Question

When you reverse the digits in a certain two-digit number you increase its value by 18.Find the number if the sum of its digits is 8.

Answer 1

Given the sum of digits of a two digit number is 8.

So, the possible combinations are 0,8 or 1,7 or 2,6 or 3,5 or 4,4.

It is given that, when digits are reversed then the difference is 18.

Let's see for which of the above combinations the difference is 18.

 

case 1:

consider 0,8

hence, 80-08=72

therefore, 0,8 is not the required combination. 

 

case 2:
consider 1,7
hence, 71-17=54
therefore, 1,7 is not the required combination.

 

case 3:
consider 3,5
hence, 53-35=18
therefore, 3,5 is  the required combination.

 

Hence, the required number is 35 and its reverse is 53.

 

This method is alternative for equations method.

 

 

Answer 2

If you have a 2 digit number represented by xy

The value is actually 10x + y

The value of the reverse is 10y + x

Example:  28 = 2(10) + 8

                82 = 8(10) + 2

 

For this problem since we know that the sum of the digits is 8:

x+y=8

 

If reversing the digits increases the value by 18 then

 

10y + x - 18 = 10x + y

subtract 10x from both sides

-9x + 10y - 18 = y

subtract y from both sides

-9x + 9y -18 = 0

add 18 to both sides

-9x + 9y = 18

 

We have two equations and two unknowns at this point:

 

equation 1)   x + y = 8

equation 2) -9x + 9y = 18

 

Multiply equation 1 through by 9 and add the equations

 

9x + 9y = 72

-9x + 9y = 18

----------------

      18y = 90

        y = 90/18

        y = 5

 

x+y = 8

x+5 = 8

x = 3

 

Your number is 35 with a reverse of 53