SOLUTION: A number with two digits is equal to four times the sum of its digits. The number formed by reversing the order of the digit is 27 greater than the given number. Find the number

A number of two digits, written "ab" has value  10a + b



4(a+b) = 10a + b              (eq 1)



Reversing the digits means writing it as "ba" which has value 10b + a:



10b + a = (10a + b) + 27      (eq 2)



Simplify both equations:

(eq 1) simplifies to  2a - b = 0  ---> b = 2a

(eq 2) simplifies to   b - a = 3  

Using substitution (b = 2a) into the simplified (eq 2)  gives

      2a - a = 3     or    a = 3   --->  b = 6

The number is 



Check:

4(3+6) = 4*9 = 36  (ok on first condition)

63 = 27 + 36    (ok on 2nd condition)