Question 1201132
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Formulate a system of equations for the situation below and solve.

A theater has a seating capacity of 750 and charges $4 for children, $6 for students, and $8 for adults. 
At a certain screening with full attendance, there were half as many adults as children 
and students combined. The receipts totaled $4600. How many children attended the show?
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<pre>
If a person is able to read and make simplest logical conclusions from the written text, 
he (or she) can immediately conclude that the number of adults was one third of 750, 
i.e. 250, while the combined number of children and students was 500.


After that, the problem can be simply reduced to one unknown and one equation.


Let x be the number of children (the major unknown in the problem).
Then the number of students is (500-x).


After that, we can write the total money equation

    4x + 6*(500-x) + 8*250 = 4600.


Simplify and find x

    4x + 3000 - 6x = 4600 - 2000

         -2x       = 4600 - 2000 - 3000

         -2x       =      -400

           x       =      {{{(-400)/(-2)}}} = 200.


<U>ANSWER</U>.  200 children.
</pre>

Solved (using single equation in one unknown).