to find the expected revenue from ticket sales

Question

Your school is holding a fete this weekend. students have been pre-selling tickets; adult tickets are $5.00, and child tickets (six years old and under) are $2.50. from past experience, you expect about 13,000 people to attend the event.

this is the first year tickets prices have been reduced for the younger children, so you really don't know how many children tickets and how many adults tickets you can expect to sell. your boss wants you to estimate the expected tiket revenue.

you consult with your student ticket-sellers, and discover that they have not been keeping track of how many tickets they have sold. they only know that they sold 548 tickets for $2460. how much revenue from each child and adult tickets can you expect?

 

can you list two methods to answer this quest, please explain too.

Answer 1

I am only dealing with part of your question in my answer. I will be addressing how to solve for the portion that has already been sold.

 

Let a = number of adult tickets

Let c = number of child tickets

 

Step 1: Figure out what equations represent your situation.

 

Dealing with quantity of tickets:

a + c = 548

 

Dealing with revenue:

5a + 2.5c = 2460

 

Step 2: Create a system of equations

Line1: a + c = 548

Line 2: 5a + 2.5c = 2460

 

Step 3: Divide "5a + 2.5c = 2460" by "5" all the way across in order to get "a" with a coefficent of 1

 

Line 2: (5a/5) + (2.5c/5) = (2460/5)

Line 2: a + 0.5c = 492

 

Step 4. Put this new Line 2 back into your system of equations.

Line 1: a + c = 548

Line 2: a + 0.5c = 492

 

Step 5: Subtract Line 2 from Line 1. One way to do this is to distribute a negative to all terms on one line and then add them together. Use whatever works for you

Line 1:  a + c =548

Line 2: -a -0.5c = -492

 

Simplify: 0 + 0.5c = 56

 

Step 6: Solve for "c".

 

c = (56/0.5)   --> c = 112

 

Step 7. Plug c = 112 back into Line 1 to solve for a

 

a + 112 = 548  --> a = 548 - 112  --> a = 436

 

Step 8. Double check your work

 

a + c = 548

436 + 112 = 548  (Yay!)

 

5a + 2.5c = 2460

5(436) + 2.5(112)  -->  2180 + 280 = 2460 (Yay!)

 

Therefore, you know a = 436 and c = 112, meaning that you sold 436 Adult tickets and 112 Child tickets.

Answer 2

Lots of words here,  Looking at some of the underlying math, if there are

a adult tickets sold for 5.00 and c child tickets for 2.50 and the number of tickets sold is represented by: 

a + c = 548 and

and the revenue for the tickets is represented by:

5.00 a + 2.50 c = 2460

 

Solve the system of equations any way you want to get (a = 436 and c = 112)

 

if you are expecting 13000 people, then this is (13,000/548) times more than the number that has been sold so far (or 23.72 times more). How much revenue would you have from 23.72 times more adult tickets and 23.72 times more child tickets?