Question
- A movie theater charges
paid an admission, the total receipts were
a. Clearly state what you are trying to find.
b. Set up a system of equations that could be used to solve the problem.
c. Solve your system algebraically. (That is, with the substitution or elimination method.)
d. Solve your system graphically. Be sure to include a sketch of your system clearly showing the
intersection point.
paid an admission, the total receipts were
a. Clearly state what you are trying to find.
b. Set up a system of equations that could be used to solve the problem.
c. Solve your system algebraically. (That is, with the substitution or elimination method.)
d. Solve your system graphically. Be sure to include a sketch of your system clearly showing the
intersection point.
Ask by Bond Lowe. in the United States
Nov 30,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the system of equations is
Solution
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Extra Insights
To determine how many adult and senior tickets were sold, we can define our variables as follows:
Let
We are interested in finding the values of
Now, we’ll set up our system of equations based on the provided information:
-
The total number of people:
-
The total amount of money earned:
To solve the system algebraically, we can utilize the substitution method. From the first equation, we can express
Now, we substitute this expression for
Now that we have
Thus, 100 adult tickets and 231 senior tickets were sold.
For the graphical solution, you would plot the two equations:
-
(This is a line with intercepts at on the y-axis and on the x-axis). -
(This line can be rewritten to find its intercepts for plotting).
The intersection point of the two lines on the graph will provide the values
Now, let’s dive into some additional fun facts about the scenario!
Movie theaters have been around since the 1890s when the first public films were shown. Originally called “nickelodeons,” they transformed the entertainment world, leading to the elaborate cinema palaces we see today. Who would have guessed that pricing and ticket sales evolve from those humble beginnings to complex systems we explore with algebra?
In today’s world, savvy theaters sometimes mix things up with dynamic pricing; this means ticket prices can vary based on the day’s demand, movie newness, and even seat selection! It’s all in the name of revenue optimization, keeping audiences engaged while keeping theaters profitable. So, the next time you buy a ticket, remember, there’s more math behind it than you might think!
