SOLUTION: If 108 attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.75 and total receipts for the concert was $351.75, how many of each went to the concert?

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Question 1026490: If 108 attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.75 and total receipts for the concert was $351.75, how many of each went to the concert?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of adults' tickets be x
Let the number of children's tickets be y


                       Money      Money
Type       Number      from       from
 of          of        EACH       ALL
ticket    tickets     ticket     tickets
-------------------------------------------
adult's        x      $3.50      $3.50x
children's     y      $2.75      $2.75y
-------------------------------------------
TOTALS       108      -----      $351.75

 The first equation comes from the second column.

  %28matrix%284%2C1%2CNumber%2Cof%2Cadult%2Ctickets%29%29%22%22%2B%22%22%28matrix%284%2C1%2CNumber%2Cof%2C%22children%27s%22%2Ctickets%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ctickets%29%29
                 x + y = 108

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

           3.50x + 2.75y = 351.75

Get rid of decimals by multiplying every term by 100:

             350x + 275y = 35175

 So we have the system of equations:
          system%28x+%2B+y+=+108%2C350x+%2B+275y+=+35175%29.

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

                   x + y = 108
                       y = 108 - x

Substitute (108 - x) for y in 350x + 275y = 35175

     350x + 275(108 - x) = 35175
     350x + 29700 - 275x = 35175
             75x + 29700 = 35175
                     75x = 5475
                       x = 73 = the number of adult tickets.

Substitute in          y = 108 - x
                       y = 108 - (73)
                       y = 35 children's tickets.

Checking:  73 adults' is $255.50 and 35 children's is $96.25
            That's 108 tickets.
            And indeed $255.50 + $96.25 = $351.75
Edwin