document.write( "Question 832454: Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots, Quentin has zero points. How many half-court shots did he make? \n" ); document.write( "
Algebra.Com's Answer #502054 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will \r\n" );
document.write( "earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots, \r\n" );
document.write( "Quentin has zero points. How many half-court shots did he make?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Let x be the number of half-court shots that Quentin makes.\r\n" );
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document.write( "Quentin has 20 attempts all together, so the number he misses will be 20 minus the number he makes,\r\n" );
document.write( "or 20-x.\r\n" );
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document.write( "He earns 20 points for each shot he makes, or 20x all together.\r\n" );
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document.write( "He loses 5 points for every shot he misses, or -5(20-x) all together.\r\n" );
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document.write( "After 20 attempts, the sum of his points is 0, so\r\n" );
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document.write( "20x - 5(20-x) = 0\r\n" );
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document.write( "Solve for x to find the number of half court shots he made. Distribute the 5 to get rid of the parentheses.\r\n" );
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document.write( "20x - 100 + 5x = 0\r\n" );
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document.write( "Combine like terms. (20x+5x is 25x.)\r\n" );
document.write( "25x - 100 = 0\r\n" );
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document.write( "Add 100 to both sides to combine constant terms. (-100+100 is 0.)\r\n" );
document.write( "25x = 100\r\n" );
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document.write( "Divide both sides by 25 to isolate the variable. (25x/25 is x.)\r\n" );
document.write( "25x/25 = 100/25\r\n" );
document.write( "x = 4\r\n" );
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document.write( "In the context of this problem, x = 4 means that Quentin made 4 half-court shots.\r\n" );
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document.write( "Let's make sure that answer makes sense. Quentin gets 20 points for every shot he makes. So he earned \r\n" );
document.write( "4*20=80 points. That left 16 misses because 20-4=16. He lost 5 points every time he missed. That's a \r\n" );
document.write( "loss of 80 points because 16*5= 80. He earned 80 points and lost 80 points. After 2 attempts, his score is 0.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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