Question 1037965
<pre><b>
Let the number of fan tickets sold be x
Let the number of students' tickets be y


                      Money       Money
Type       Number      from       from
 of          of        EACH        ALL
ticket     tickets    ticket     tickets
-------------------------------------------
fans'          x      $5.00       $5.00x
students'      y      $1.50       $1.50y
-------------------------------------------
TOTALS       310      -----    $1119.50

The first equation comes from the "Number of tickets" column.

  {{{(matrix(3,1,Number,of,fans))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,students))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,tickets))}}}

                   x + y = 310

 The second equation comes from the "Money from all tickets" column.
  {{{(matrix(5,1,Money,from,ALL,fan,tickets))}}}{{{""+""}}}{{{(matrix(5,1,Money,from,ALL,"students'",tickets))}}}{{{""=""}}}{{{(matrix(5,1,Total,money,from,ALL,tickets))}}}

           5.00x + 1.50y = 1119.50

Get rid of decimals by multiplying every term by 10:

               50x + 15y = 11195

 So we have the system of equations:
           {{{system(x + y = 310,50x + 15y = 11195)}}}.

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

           x + y = 310
               y = 310 - x

Substitute (310 - x) for y in 50x + 15y = 11195

   50x + 15(310 - x) = 11195
    50x + 4650 - 15x = 11195
          35x + 4650 = 11195
                 35x = 654
                   x = 187 = the number of fan tickets.

Substitute in y = 310 - x
              y = 310 - (187)
              y = 123 students' tickets.

Checking:  187 fan tickets brought in $9350 and 123 students' tickets
            brought in $184.50.  That's 310 tickets.
            And indeed $9350 + $184.50 = $1119.50
Edwin</pre></b>