Question 1018857

<pre>
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.

  {{{(matrix(4,1,Number,of,"children's",tickets))}}}{{{""+""}}}{{{(matrix(4,1,Number,of,adult,tickets))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,tickets))}}}

                 x + y = 50

 The second equation comes from the last column.
  {{{(matrix(5,1,Money,from,ALL,"children's",tickets))}}}{{{""+""}}}{{{(matrix(5,1,Money,from,ALL,adult,tickets))}}}{{{""=""}}}{{{(matrix(4,1,Money,from,ALL,tickets))}}}


            5x + 10y = 350

 So we have the system of equations:
           {{{system(x + y = 50,5x + 10y = 350)}}}.

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</pre>