Question

the sum of the digits of a two digit number is 8 when the digits are reversed the number increases by 36 find the original number

Answer 1

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Let the two digit number be xy

 

x + y = 8

 

Right away I can logically see that, since the value

increases if the digits are reversed, our choices are:

17

26

35

 

If I reverse 17 I get 71 .. This is more than an 18 increase

If I reverse 26 I get 62 ... This is more than an 18 increase

If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer

 

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Now algebraically:

x + y = 8   {equation 1}

 

The value of xy is 10x + y

The value of yx is 10y + x

 

10y + x = 10x + y + 18 

9y - 9x = 18

9(y - x) = 18

y - x = 2

 

From equation 1: y = 8-x

 

8 - x - x = 2

8 - 2x = 2

-2x = -6

x = 3

 

y - x = 2

y - 3 = 2

y = 5

 

Original number xy = 35

Answer 2

let the ones digit no=x
tens digit no=y
no=10y+x

x+y=8

10x+y=10y+x+36