document.write( "Question 1107211: Formulate a system of equations for the situation below and solve.\r
\n" ); document.write( "\n" ); document.write( "A theater has a seating capacity of 900 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 $5200. How many children attended the show? \n" ); document.write( "

Algebra.Com's Answer #722257 by ikleyn(52914) $\"\"$ $\"About$

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\n" ); document.write( "Formulate a system of equations for the situation below and solve.\r
\n" ); document.write( "\n" ); document.write( "A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults.
\n" ); document.write( "At a certain screening with full attendance, there were half as many adults as children and students combined.
\n" ); document.write( "The receipts totaled $5200. How many children attended the show?
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document.write( "Since \"there were half as many adults as children and students combined\", you can momentarily conclude that there were 300 adults \r\n" );
document.write( "(1/3 of the full capacity) and 600 children and students combined (2/3 of the full capacity).\r\n" );
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document.write( "Let C be the number of children.\r\n" );
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document.write( "Then the number of students was  (600-C).\r\n" );
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document.write( "The \"value\" equation for the receipts totaled is THIS:\r\n" );
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document.write( "4C + 6*(600-C) + 8*300 = 5200      dollars.\r\n" );
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document.write( "    *** One single equation for one single unknown. ***\r\n" );
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document.write( "4C + 3600 - 6C + 2400 = 5200\r\n" );
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document.write( "-2C = 5200 - 2400 - 3600 = -800  ====>  C = 400.\r\n" );
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document.write( "Answer.  400 children.\r\n" );
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\n" ); document.write( "Notice. This problem is for one single equation, actually.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, my major wish was do not make it more complicated than it really should be.\r
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