Story problems.

Question

Please show the work as I need to know how to get the answer.  

The school that Emily goes to is selling tickets to a spring Musical. On the first day of ticket sales the school sold one adult ticket and 7 student tickets for a total of $42. The school took in $132 on the second day by selling 6 adult tickets and 12 student tickets. What is the price of each one adult ticket and one student ticket?

Answer 1

a represents the price of an adult ticket

s represents the price of a student ticket

 

a + 7s = 42

6a + 12s = 132

 

6a + 42s = 252        multiply both sides of top equation by 6

6a + 12s = 132

 

30s = 120                subtract bottom from top

s = 4                        divide both sides by 30

 

Student tickets cost $4.

 

You can determine the cost of an adult ticket.

Answer 2

It is important to get the units correct.   (number of tickets)*(dollars per ticket) = dollars

 

Let:

  x = number of adult tickets

  y = number of student tickers

 

First day:

     dollars for adult tickets    +    dollars for student tickets     =     $42

          (1)(x)                        +                (7)(y)                    =      $42   [eq1]

 

Second day:

    dollars for adult tickets    +    dollars for student tickets     =     $132  

          (6)(x)                        +               (12)(y)                  =      $132   [eq2]

 

Now, you may use either substitution or elimination (let's use substitution):

     x = 42-7y          [from eq1]

     6(42-7y) + 12y = 132          [substitute for x in eq2]

     252 - 42y + 12y = 132         [distribute]

      -30y = -120                       [collect terms; subtract 252 from each side]

         y = 4                              [divide both sides by (-30)]

 

       x + 7y = 42             [eq1 again; we could use either equation]

       x + 7(4) = 42

       x = 14

 

Each adult ticket costs $14 and each student ticket costs $4.

 

Check:

   Is  (1)*($14) + (7)($4) = $42   ?

          $14 + $28 = $42   ?

             $42 = $42   ?yes

   Is  (6)($14) + (12)($4) = $132   ?

         $84 + $48 = $132   ?

             $132 = $132   ?yes