What's the equation?

Question

Mercedes saves $50 each month. Ken saves $40 each month, and he started with $100. After how many months will they have the same amount saved?

Answer 1

Word (story) problems are easy if you use a table to translate the words to precise, concise math variables and operations.  For example,
       Is                 means                          =
     Larger than, more than                      +
      Four times x                                    4*x
     F is 550 less than S                       F = S – 550
       Total of A, B, C; altogether          A + B + C 
      If                                              a partial answer
This seems obvious – until you get stuck on a word problem.

So, assign variables: 
   Let M = Mercedes’ total savings to date
          K = Ken’s total savings to date
          N = after how many months; number of the month you are interested in 

 Now, translate:
   “Mercedes saves $50 each month”         means          M = $50 * N
   “Ken saves $40 each month, and he started with $100”   

                                            means       K = $40 * N  + $100
   “After how many months will they have the same amount saved?”  

                                            Means     At what N will M=K  ?
 
Now, the easy math:
        M  =  K
     $50*N = $40*N+$100
Well, I said it was easy.  So, solve for N to answer the question.
 
Then, always check your answer:
   Is   $50*10 = $40*10 + $100   ?     Yes.

Answer 2

Let after x months Mercedes and Ken save the same amount.

 

Therefore 50x = 40x +100

              50x - 40x = 100

              10x          = 100

                  x           = 100/10

                 x           = 10

After 10 months  Mercedes and Ken  will save the same amount.