The value of n is both 5 times as much as the value of m and 36 more than the value of m what are the values of n & m

 " M = 9  ;  N = 45 " .


Note:  Assume that "n" = "N' ;  that is, "assume that "N" is another way to write: "n" ; 

        →  n = 5 M ;

        →  n = 36 + M ;

Find "n" and "m" ;

Note:  n = 5 M  =  36 + M ;  

        →  5 M  =  36 + M ;

Subtract "M" from EACH SIDE of the equation ; 

       →  5 M  −  M  =  36  +  M  − M ; 

to get: 
    
          →  4 M  =  36  ;

Now, divide EACH SIDE of the equation by "4" ;

          →  4 M / 4  =  36 / 4  ;
 
 to get:

          →  M = 9 ;

The value of "M" = 9 ;

Now, let us find the value for "N" ;

Note:   " n = 5 M  =  36 + M " ; 

1)  n = 5 M ;  Our calculated value for "M" is "9" ; 

so, we plug in "9" for "M" ; to solve for "N" ;

   N = 5(9) = 45 ;

  N = 45 ;

2)  We can "check our answer", as follows:

        →  Note:   " n = 5 M  =  36 + M " ; 

N = 36 + M ;   We have calculated "N" to be "45" .
                  
                       We have calculated "M" to be "9" ; 

So, when we plug in "9" for "M" in this equation; our value for "N" should be:
    "45" ; 

N = 36 + 9 ; 

N = 45 ?  Yes! 

So, the answer is:  " M = 9  ;  N = 45 " .

No solution : there is no number of boxes that she bought