Algebra.Com's Answer #738613 by ikleyn(52908)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "A theater has a seating capacity of 1050 and charges $3 for children, $5 for students, and $7 for adults.
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document.write( "At a certain screening with full attendance, there were half as many adults as children and students combined.
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document.write( "The receipts totaled $5150. How many children attended the show?
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document.write( " The solution by @josgarithmetic was WRONG starting from his very first equation,\r
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document.write( " so I came with the correct solution.\r
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document.write( " For your safety, simply ignore writing by @josgarithmetic.\r
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document.write( "Let x =# of children, y = # of students and z = # of adults.\r\n" );
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document.write( "Then you have this two equation\r\n" );
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document.write( "x + y + z = 1050 (1) (the total) and\r\n" );
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document.write( "z =  (2) (\"there were half as many adults as children and students combined.\")\r\n" );
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document.write( "Substitute eq(2) into eq(1), replacing z. You will get\r\n" );
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document.write( "x + y +  = 1050, or\r\n" );
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document.write( " = 1050, which gives you \r\n" );
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document.write( "x + y =  = 700.\r\n" );
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document.write( "So, you know now that the combined number of children and students was 700.\r\n" );
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document.write( "You also know that the number of adults was 1050 - 700 = 350.\r\n" );
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document.write( "So, adults payed 350*7 = 2450 dollars;\r\n" );
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document.write( "then children and students payed 5150 - 2450 = 2700 dollars for their tickets.\r\n" );
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document.write( "Now you have this system of 2 equations in 2 unknowns\r\n" );
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document.write( " x + y = 700, (2)\r\n" );
document.write( "3x + 5y = 2700. (3)\r\n" );
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document.write( "Thus you reduced the original problem from 3 unknowns to only 2 unknowns\r\n" );
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document.write( "Now solve the system (2),(3) by substitution method. From eq(1) express y = 700 - x and substitute it into eq(2). You will get\r\n" );
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document.write( "3x + 5*(700-x) = 2700\r\n" );
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document.write( "3x - 5x = 2700 - 3500\r\n" );
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document.write( "-2x = -800 ====> x = 400.\r\n" );
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document.write( "The number of children was 400; the number of students was 700-400 = 300; the number of adults was 350.\r\n" );
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document.write( "Solved.\r
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