# 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...

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?

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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.

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

Let the number of adult tickets sold be x . Then the number of student tickets being 4 more than the adults is x+4.

The amount from adult tickets is = number of tickets sold * rate = x*3.5 = $3.5x.

The amount due to sale of student tickets= $(x+4)2.5 = 2.5(x+4).

Algebraical sum of the amount due to sale of adult and student tickets = $(3.5x+2.5(x+4)) = $(6x+10) which is equal to the actual amount =$ 58. So

6x+10 = 58. Or

6x = 58 -10 =48. Or

x = 48/6 = 8 is the number of adult tickets sold. Therefore the number of student tickets sold = x+4 = 8+4 =12.

Let's put x=number of tickets sold, with the price for adults, 3.5$

y = number of tickets sold, with the price for students, 2.5$

Equation for: sold 4 more student tickets than adult tickets.

y=4+x (1)

Total in sales:

3.5x+2.5y=58

35x+25y=580

We'll divide by 5:

7x+5y=116

We'll substitute (1) and we'll get:

7x + 5(4+x)=116

7x + 20 + 5x = 116

12x = 116-20

12x = 96

We'll divide by 4:

3x = 24

**x = 8 tickets for adults**

y = 8+4

**y = 12 tickets for students**