Question
Tickets for the school play cost
for adults and
for students. 120 tickets were sold in all for
. The equations for total profit and total tickets are as follows:
and
tickets, where
is the number of students and
is the numt
of adults.
of adults.
Ask by Schultz Nunez. in the United States
Jan 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There were 80 student tickets and 40 adult tickets sold.
Solution
To determine the number of student and adult tickets sold for the school play, we’ll solve the system of equations provided:
Where:
-
= Number of student tickets sold -
= Number of adult tickets sold
Step 1: Simplify the Equations
First, let’s simplify the revenue equation by dividing all terms by 5 to make the calculations easier:
Now, our system of equations looks like this:
Step 2: Subtract Equation (2) from Equation (1)
Subtracting equation (2) from equation (1) helps eliminate
:
Step 3: Substitute
Back into Equation (2)
Now that we know
, substitute this value back into equation (2) to find
:
Step 4: Conclusion
- Number of Student Tickets Sold (
): 80 - Number of Adult Tickets Sold (
): 40
Verification
To ensure the solution is correct, let’s verify it against the original revenue equation:
The total revenue matches the given amount of $800, confirming that the solution is correct.
Summary
- Student Tickets Sold: 80
- Adult Tickets Sold: 40
Answered by UpStudy AI and reviewed by a Professional Tutor
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Bonus Knowledge
Did you know? The classic school play has a fascinating history! It dates back to medieval times when morality plays were performed to teach moral lessons. Over time, these performances evolved into the vibrant school productions we see today, encouraging creativity, teamwork, and public speaking among students. So, the next time you enjoy a school play, remember you’re witnessing a tradition that’s centuries old!
Now, if you’re tackling these types of equations, a common mistake is mixing up your variables. Make sure you clearly define what each variable represents (like
for students and
for adults) to avoid confusion. Draw a quick sketch or a diagram if it helps visualize the problem. And remember, double-check that your equations represent the situation correctly—small errors can lead to big headaches down the line!