THE SUM OF THE DIGITS OF A 2-DIGIT NUMBER IS 10. THE NUMBER OBTAINED BY INTERCHANGING THE DIGITS EXCEEDS THE ORIGINAL NUMBER BY 36.FIND THE...

Firstly we have rewrite the word problem into Mathematical form: 

Let's assume :

x = the 10's digits

y = units

Then the original number: 

10x + y = two digit number

Now lets write down what's given in the problem: 

x + y = 10  

Re-written as: y= 10 -x (equation 1)

We are also told the number obtained by interchanging the two digits exceeds the number by 36:

interchanged = original + 36

10y + x = 10x + y + 36

9y = 9x + 36

y = x + 4

Now equate the above equation to equation 1 

10 - x = x +4

2x = 6

x = 3

Now find y:

x+ y =10

y= 10 - 3

y = 7

Now we are required to find the original number. From above the equation of the original number is: 

10x + y = 10(3) + 7 =37

The original number is 37