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?

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) (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.

  
                 x + y = 108

 The second equation comes from the last column.
  

           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:
          .

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

RELATED QUESTIONS
If 68 people attend a concert and tickets for adults cost $3.75 while tickets for... (answered by mananth,MathLover1,math_tutor2020)

If 72 people attend a concert and tickets for adults cost $3.5 while tickets for children (answered by josgarithmetic)

If 110 people attend a concert and tickets for adults cost $3.5 while tickets for... (answered by math_tutor2020,josgarithmetic)

If 129 people attend a concert and tickets for adults cost $2.25 while tickets for... (answered by ikleyn,josgarithmetic,math_tutor2020)

If 122 people attend a concert and tickets for adults cost $4 while tickets for children... (answered by stanbon)

If 90 people attend a concert and tickets for adults cost $3.75 while tickets for... (answered by ikleyn)

If 118 people attend a concert and tickets for adults cost $3.75 while tickets for... (answered by ikleyn)

If 109 people attend a concert and tickets for adults cost $4 while tickets for children... (answered by richwmiller)

If 126 people attend a concert and tickets for adults cost $3 while tickets for children... (answered by josmiceli,macston)