Tickets to a concert cost $9.00 for adults and $6.50 for students. A total of 950 people paid $7675.00 to

Question

Tickets to a concert cost $9.00 for adults and $6.50 for students. A total of 950 people paid $7675.00 to
attend. How many students attended the concert.

Answer 1

 

Let:

  a = number of adults attending

  s = number of students attending

 

  a + s = 950   (1)  (given)

  9a + 6.5s = 7675   (2)   (cost per adult * number of adults + cost per student * number of students = total amount spent)

 

Looking for s.   Multiply (1) by 9 then subtract eq (2), this will eliminate the variable a:

 

   (1)  9a  + 9s     = 8550

-  (2)  9a  + 6.5s  = 7675  

-------------------------------

          0a  + 2.5s  = 875

 

                    s  = 875/2.5  = 350 students

 

 

Check:

    From (1),  350 students implies  950 - 350 = 600  adults

      9*600 + 6.5*350  =  7675.

 

 

 

Answer 2

Let a be the number of adults and s the number of students.

 

Now a + s = 950 => a = 950 - s

 

Also, 9a + 6.5s = 7675.

 

Substitute the first equation into the second:

 

9(950 - s) + 6.5s = 7675

8550 - 9s +6.5s = 7675

2.5s = 875

s = 350

 

There were 350 students and 600 adults.