Find the price of an adult ticket and the price of a child ticket.

Question

Bill's school is selling tickets to a choral performance. On the first day of ticket sales the school
sold 7 adult tickets and 5 child tickets for a total of $119. The school took in $136 on the second
day by selling 9 adult tickets and 4 child tickets.

Answer 1

The problem asks that we find $ for adult ticket (A) and for child ticket (C).  And, Dollars = number of tickets* ($/ticket)..

 

First day:        7A + 5C = 119   or   63A + 45C = 1071      (multiplied by 9)

Second day:    9A + 4C = 136   or   63A + 28C =  952       (multiply by 7)

                                                    ----------------------

                                                     0     + 17C = 119        (subtract equations)

                                                                  C = $7          (divide both sides by 17)

                     7A + 5(7) = 119      (put C=7 into first equation)

                        7A =  84              (subtract 35 from both sides)

                          A = $12             (divide both sides by 7)

Check:

      Is 7(12) + 5(7) = 119  ?

             84 + 35  = 119  ?   yes

      Is 9(12) + 4(7) = 136   ?

           108 + 28 = 136   ?    yes

Answer 2

If you are trying to figure out the price of an adult ticket and a child ticket, here are the answers:

 

1 adult ticket= $12

1 child ticket= $7 

check:

7 x $12= $84

5 x $7= $35

$84 + $35= $119

 

Trial and error is one of the easiest ways to figure out this problem.