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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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.

  %28matrix%284%2C1%2CNumber%2Cof%2C%22children%27s%22%2Ctickets%29%29%22%22%2B%22%22%28matrix%284%2C1%2CNumber%2Cof%2Cadult%2Ctickets%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ctickets%29%29

                 x + y = 50

 The second equation comes from the last column.
  %28matrix%285%2C1%2CMoney%2Cfrom%2CALL%2C%22children%27s%22%2Ctickets%29%29%22%22%2B%22%22%28matrix%285%2C1%2CMoney%2Cfrom%2CALL%2Cadult%2Ctickets%29%29%22%22=%22%22%28matrix%284%2C1%2CMoney%2Cfrom%2CALL%2Ctickets%29%29


            5x + 10y = 350

 So we have the system of equations:
           system%28x+%2B+y+=+50%2C5x+%2B+10y+=+350%29.

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