Aisha is going to ship some gifts to family members, and she is considering two shipping companies. The first shipping company charges a fee of $10 to ship a medium box, plus an additional $7 per kilogram. A second shipping company charges $15 for the same size of the box, plus an additional $6 per kilogram. At a certain weight, the two shipping methods will cost the same amount. What is that weight? How much will it cost?

Answer Step-by-step explanation:

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                                   +

     Four times a                           4*a

    F is 550 less than S                F = S – 550

      Total of A, B, C                       A + B + C  

This seems obvious – until you get stuck on a word problem.  So,

 “the first company” ,  “a second company”      becomes       Let their costs be F and S

                                                                                                 Let K be the number of kilograms

  “$20 to ship a medium box, plus an additional $2 per kilogram”           F =  $20 + 2*K

   “10 for the same size of box, plus an additional $3 per kilogram”           S  =  $10 + 3*K

  “the two shipping methods will cost the same amount”                               F = S

 “What is that weight?”                                                                             report K

Now, the math:

        F        =        S

  20 + 2K   =   10 + 3K

     $10  =  K