document.write( "Question 1185268: In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Jim made 73 more 2-point field goals that 3-point field goals. If he scored a total of 216 goals in the tournament how many 3-point field goals did he make? \r
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Algebra.Com's Answer #816062 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament,
\n" ); document.write( "Jim made 73 more 2-point field goals that 3-point field goals. If he scored a total of 216 goals in the tournament
\n" ); document.write( "how many 3-point field goals did he make?
\n" ); document.write( "2x+3y=216
\n" ); document.write( "2x+73=3y
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\n" ); document.write( "\n" ); document.write( " According to the terminology, used in the problem, you should DISTINCT the goals and the points.\r
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\n" ); document.write( "\n" ); document.write( " To distinct them is IMPORTANT to write equation correctly.\r
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document.write( "The system of equation in your post is INCORRECT (is inadequate to the problem).\r\n" );
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document.write( "The correct system is THIS\r\n" );
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document.write( "    2x + 3y = 216    (1)\r\n" );
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document.write( "    x = y + 73       (2)\r\n" );
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document.write( "To solve the system, substitute expression (2) for x into equation (1).  You will get then\r\n" );
document.write( "a single equation fot y, which is the unknown variable under the problem's question\r\n" );
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document.write( "    2*(y + 73) + 3y = 216\r\n" );
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document.write( "Simplify and find y\r\n" );
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document.write( "    2y + 146 + 3y = 216\r\n" );
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document.write( "    2y + 3y       = 216 - 146\r\n" );
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document.write( "       5y         =    70\r\n" );
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document.write( "        y         =    70/5 = 14.\r\n" );
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document.write( "ANSWER.  14 3-score goals.\r\n" );
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