Instead of doing your problem, here is another one EXACTLY like yours
in every way for you to use as a model in doing yours:

t = tens digit
u = units digit
10t+u = the two-digit number
t+u = sum of digits

units digit = tens digit + 5
      u     =     t      + 5

u = t + 5

The number = 3 times sum of digits
  10t+u    = 3   ∙     (t+u)

10t + u = 3(t + u)

Substitute t + 5 for u in

    10t + u = 3(t + u)

10t + t + 5 = 3(t + t + 5)

    11t + 5 = 3(2t + 5)

    11t + 5 = 6t + 15
     
         5t = 10

          t = 2

Substitute 2 for t in  

          u = t + 5
        
          u = 2 + 5

          u = 7

The tens (first) digit is 2 and the units (second) digit is 7.

So the number is 27.

Now do your problem the exact same way.

Edwin

Following to the hint, we write 

    N = 10r + u.         (1)


We are given that  

    u = r+3              (2)

and

    N = 4*(r + u).       (3)


Replace N in the left side of (3) by 10r + u, according to (1).

    10r + u = 4r + 4u.    (4)


Replace "u" in both sides of (4) by (r+3), based on (2).  You will get then

    10r + (r+3) = 4r + 4*(r+3).


Simplfy and find "r"

    10r + r + 3 = 4r + 4r + 12

    11r + 3 = 8r + 12

     11r - 8r = 12 - 3

     3r       = 9

      r       = 9/3 = 3.


Thus r = 3  and  u = r+3 = 3+3 = 6.


Hence, the number is  10r+u = 10*3 + 6 = 36.


ANSWER.  The number is 36.

Let tens and units digits, be T and U, respectively

Then we get: U = T + 3 ------ eq (i)

Also, 

2T = T + 3 ------ Substituting 2T for U in eq (i)

2T - T = 3

T, or tens digit = 3



U = 3 + 3 ------ Substituting 3 for T in eq (i)

U, or units digit = 6

 

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!
 


Apparently, with the hint that is given, the problem is supposed to be solved using formal algebra.  You have a couple of responses showing good examples of that.


But you can get good mental exercise (and learn a lot about solving math problems) by solving the problem quickly using logical reasoning and some simple mental arithmetic.


In this problem, we know the units digit is 3 more than the tens digit. 


The only possible numbers are 14, 25, 36, 47, 58, and 69.


We know the number itself is a multiple of 4.


Using basic divisibility rules, it is easy to see that only one of the possible numbers -- 36 -- is divisible by 4.


ANSWER: The number is 36.


 

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