SOLUTION: A total of 431 tickets were sold to a concert, bringing in a total of $5,332. Two types of tickets were sold: adult tickets were sold for $14 each and student tickets were sold for

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Question 1100755: A total of 431 tickets were sold to a concert, bringing in a total of $5,332. Two types of tickets were sold: adult tickets were sold for $14 each and student tickets were sold for $8 each. How many adult tickets were sold?
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
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.

-----------------
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.



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