SOLUTION: A total of 50 tickets were sold for a play. Children tickets cost $5 and adult tickets cost $10. If the total sold was $350, how many tickets of each type were sold

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Question 1018857: A total of 50 tickets were sold for a play. Children tickets cost $5 and adult tickets cost $10. If the total sold was $350, how many tickets of each type were sold
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Let the number of children's tickets be x
Let the number of adult's tickets be y


                      Money      Money
Type       Number     from       from
 of          of       EACH       ALL
ticket    tickets    ticket     tickets
-------------------------------------------
children    x           $5      $5x
adults      y          $10     $10y
-------------------------------------------
TOTALS     50        -----     $350

 The first equation comes from the second column.

  

                 x + y = 50

 The second equation comes from the last column.
  


            5x + 10y = 350

 So we have the system of equations:
           .

We solve by substitution.  Solve the first equation for y:

           x + y = 50
               y = 50 - x

Substitute (50 - x) for y in 5x + 10y = 350

  5x + 10(50 - x) = 350
   5x + 500 - 10x = 350
        -5x + 500 = 350
              -5x = -150
                x = 30 = the number of children's tickets.

Substitute in y = 50 - x
              y = 50 - (30)
              y = 20 adult tickets

Checking:  30 childrens is $150 and 20 adults is $200
            That's 50 tickets.
            And indeed $150 + $200 = $350
Edwin
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