Last Tuesday cinemas sold a total of 8,500 tix for new movie. Proceeds $64,600. Tickets 3 ways: matinee admit $5, student admit $6 all day, reg admit $8.50.

Question

Last Tuesday cinemas sold a total of 8,500 tix for new movie. Proceeds $64,600. Tickets 3 ways: matinee admit $5, student admit $6 all day, reg admit $8.50.

How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

Also, if the number of tickets sold last Tuesday reflects a 3.7% increase from the same day last week, how many tickets were sold on that prior Tuesday?

Answer 1

Let z=Students, M=Matinee, and R=Reg

 

To set up the equations, first look at the price.

Since we don't know how many of each for each price, we associate a letter with the value.

For example: 5z=$10 therefore z=2. 2 Matinee bought tickets.

 

64600=5M + 6z + 8.5R

 

We also know twice as many student tickets were sold as matinee

 

2M = z

 

We also know total number of tickets.

 

8500 = M + z + R

 

Note:  Good rule of thumb. You have to have the same number of equations as there are unknowns.

 

We have now have 3 equations and 3 unknowns.

 

64600=5M + 6z + 8.5R

2M = z

8500 = M + z + R

 

Now just solve for each unknown as you see fit.

 

As for the second part of the question, it's just a simple percentage problem.

3.7%=.037

They are looking the original value so if this week is 8500 and there was an increase, then we know x will be less than 8500.

To keep math simple, we'll add 100% to the 3.7%

1.037x=8500

x=8197 rounding up.

There were about 8197 tickets sold the prior Tuesday.

 

Answer 2

let m = the number of matinee tix at $5 each

let s = the number of student tix at $6 each

let r = the number of regular tix at $8.50 each

 

The revenue total is 64,600 = 5m + 6s + 8.5r on Tuesday; also, m + s + r = 8,500

 

s =2m <--- number of # student tix is twice the number of matinee tix.

 

This is three equations in three unknowns.  When you replace s by 2m, you have two equations in two unknowns...a standard algebra problem.  Solve by the "elimination" method or other methods if you know them. Check your work. The numbers for m, s & r must all be integers (non-negative).