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?
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
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.
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.
Total in sales:
We'll divide by 5:
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