.
Let A be the number of adults tickets.
Then the number of student tickets is (431-A).
Adults tickets cost 14*A dollars (do you understand why ?)
Student tickets cost 8*(431-A) dollars (do you understand why ?)
In all, the tickets cost 14*A + 8*(431-A) dollars (do you understand why ?)
This sum is equal to 5332 dollars, according to the condition, and it gives you an equation
14*A + 8*(431-A) = 5332.
It is your major/basic equation, so called "money" equation.
Why do we call it "the money equation" ? - Because it is based on counting money.
As soon as you got this equation (and understood it), the setup part is completed.
To solve the equation, simplify it step by step:
14A + 3448 - 8A = 5332 ====> 6A = 5332 - 3448 = 1884 ====> A = = 314.
Answer. 314 adults tickets were sold.
Solved.
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This problem can be solved by other methods, too.
See the lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.