the sum of two digit number is 15. The digits are reversed, new number is 9 more than the original number. what is the original number?

Question

the sum of the digits in a two digit number is 15. When the number is 9 more than the original number. What is the orginal number?

 

Answer 1

Note: The value of a 2 digit number xy 

is found by 10x + y

Example: 67 = 10(6) + 7

 

x + y = 15   {equation 1}

 

10y + x = 10x + y + 9  {equation 2}

 

from equation 1: y = 15-x

Substitute into equation 2

 

10(15-x) + x = 10x + 15 - x + 9

150 - 9x = 9x + 24

126 = 18x

x = 7

y = 8

 

The 2 digit number is 78

 

 

Answer 2

Let digit at unit place is x

digit at tens place is y

 

Number = 10y+x

 

so x+y =15   ______________eq 1

 

If number reversed

digit at unit place is y

digit at tens place is x

 New Number : 10x +y

 

new number is 9 more than the original number

 

10x +y = 10y+x +9

 

9x-9y =9

x-y=1________eq 2

 

x=1+y

 

substitute  x=1+y in eq 1

 

x + y =15

1+y +y =15

 

1+2y =15

2y =14

y=7

 

so x =8

 

So original number is 78