SOLUTION: The cost to attend a college baseball game is $5 except for students, who are admitted for $1.50. Yesterday’s game was attended by 310 fans and the college collected $1119.50. How

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Question 1037965: The cost to attend a college baseball game is $5 except for students, who are admitted for $1.50.
Yesterday’s game was attended by 310 fans and the college collected $1119.50. How many students
attended the game?
Found 2 solutions by addingup, Edwin McCravy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the general public and y be students.
x+y = 310 subtract y from both sides
x = 310-y We'll use this value for x
5x+1.50y = 1119.50
5(310-y)+1.50y = 1119.50
1550-5y+1.50y = 1119.50
-3.50y = -430.50 Divide, and remember -/- = +
y = 123
123 students attended the game

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

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.

  %28matrix%283%2C1%2CNumber%2Cof%2Cfans%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cstudents%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ctickets%29%29

                   x + y = 310

 The second equation comes from the "Money from all tickets" column.
  %28matrix%285%2C1%2CMoney%2Cfrom%2CALL%2Cfan%2Ctickets%29%29%22%22%2B%22%22%28matrix%285%2C1%2CMoney%2Cfrom%2CALL%2C%22students%27%22%2Ctickets%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cmoney%2Cfrom%2CALL%2Ctickets%29%29

           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%28x+%2B+y+=+310%2C50x+%2B+15y+=+11195%29.

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