How would you come up with an equation and solve for the following problem? Jenny sold tickets for the annual spring concert at Middletown High School. The concert tickets cost $3.50 for adults and $2.50 for students. If Jenny sold 4 more student tickets than adult tickets and she has a total of $58.00 in sales, how many of each type of ticket did she sell?

Expert Answers

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The cost per ticket for adult =Ca= 3.5

the cost per ticket for student = Cs= 2.5

number of students tickets sold = 4 more than adults tickets

      s= 4 + a....... (1)

the total sale = (3.5)a+ (2.5)s = 58.....(2)

sustitute with equatin (1)

==> (3.5)a + (2.5)...

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The cost per ticket for adult =Ca= 3.5

the cost per ticket for student = Cs= 2.5

number of students tickets sold = 4 more than adults tickets

      s= 4 + a....... (1)

the total sale = (3.5)a+ (2.5)s = 58.....(2)

sustitute with equatin (1)

==> (3.5)a + (2.5) (4+a)= 58

==> (3.5)a+ 10+ (2.5)a = 58

==> 6a +10= 58

==> 6a = 48

==> a = 8  ==> s = 12

then she sold 8 adults tickets and 12 students tickets

 

 

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

She sold 8 adult tickets and 12 student tickets.  Here is how to set this up and solve it.

Let A be the adult tickets and S the student tickets. A = S + 4 because she sold 4 more student tickets.

3.5A + 2.5(A +4) = 58

This is because you have to take the adult tickets times their price and add that to the student tickets times their price.

3.5A + 2.5A + 10 = 58

6A = 48

A = 6

So she sold 6 adult tickets.  They would have cost a total of $28.

If she sold 6 of those, she sold 12 student tickets.  They would have cost $30.

Together, that is $58.

 

 

Approved by eNotes Editorial Team