Question 1196502
.
a gathering of 600 people for a children's concert generated $4000 in revenue 
from the sale of tickets in which each adult was charged $7 and each child 
was charged $5 each. How many children were there?
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<pre>
x = the number of children

600-x = the number of adults.


Write the revenue equation (total money collected)

    5x + 7*(600-x) = 4000  dollars.


Simplify and find x

    5x + 4200 - 7x = 4000

    5x - 7x        = 4000 - 4200

      -2x          =    -200

        x          = {{{(-200)/(-2)}}} = 100.


<U>ANSWER</U>.  100 children.


<U>CHECK</U>.  100*5 + 7*(600-100) = 500 + 3500 = 4000 dollars total, confirming the answer.
</pre>

Solved.


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It is a standard and typical tickets problem.


There are different methods of solving such problems.
In this site, there is a lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-Tickets.lesson>Using systems of equations to solve problems on tickets</A> 

explaining and showing different methods of solving such problems.


From this lesson, &nbsp;learn on how to solve such problems once and for all.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Systems of two linear equations in two unknowns</U>".


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.