hard word problem

Question

At her birthday party, Sam is serving a slice of cake to each attendee. If each attendee receives 2 slices, there will be 20 slices left. If 5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left. How many attendees were at the party?

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 a                                    4*a
     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.  Since we are asked to find the number of attendees, let N = number of attendees
   “each attendee receives 2 slices”                    means                          2*N slices
   “20 slices left”                                                   means                       20
  “each attendee receives 2 slices, there will be 20 slices left”     means        slices = 2*N + 20
   “5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left”
                                                                        Means                5 slices for N-5 attendees
                                                                                       Slices = 5 * (N-5)

O.K., now the math:
        Slices =  2*N + 20  =  5 * (N-5)
                       2N + 20  = 5N – 25
                               45  = 3N
                                15 = N

Checking:
    Does  2*(15) +20  =  5*(15-5)     ?   Yes.

Answer 2

Just kind of a weird wording for an easy algebra problem.....let equations do all the work!!!!!

 

A = number of attendees.

 

2*A + 20 would be all the slices of scenario 1

5(A-5) would be the representation for situation 2

 

So 2A+20 = 5(A-5)

     2A + 20 = 5A -25

             45 = 3A

             15 = A

 

You can go back and check that this really worked. Hope this helped