document.write( "Question 1007322: Ms. snow decide to get a test worth 90 points and contains 25 questions. multiple-choice questions are worth 3 points and word problems are worth 4 points. How many of each type of question are there? \n" ); document.write( "

Algebra.Com's Answer #623263 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "Let the number of multiple choices be x\r\n" );
document.write( "Let the number of word problems be y\r\n" );
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document.write( "                                 Value        Value\r\n" );
document.write( "Type               Number          of          of\r\n" );
document.write( " of                  of           EACH         ALL\r\n" );
document.write( "question         questionss     question    questions\r\n" );
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document.write( "multiple choices     x             3            3x\r\n" );
document.write( "word problems        y             4            4y\r\n" );
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document.write( "TOTALS              25          -----           90\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
document.write( "                 x + y = 25\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "               3x + 4y = 90\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 25\r\n" );
document.write( "               y = 25 - x\r\n" );
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document.write( "Substitute (25 - x) for y in 3x + 4y = 90\r\n" );
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document.write( "     3x + 4(25 - x) = 90\r\n" );
document.write( "      3x + 100 - 4x = 90\r\n" );
document.write( "          -1x + 100 = 90\r\n" );
document.write( "                -1x = -10\r\n" );
document.write( "                  x = 10 = the number of multiple choices.\r\n" );
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document.write( "Substitute in y = 25 - x\r\n" );
document.write( "              y = 25 - (10)\r\n" );
document.write( "              y = 15 = the number of word problems.\r\n" );
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document.write( "Checking:  10 multiple choices is 30 and 15 word problems is 60\r\n" );
document.write( "            That's 25 questions.\r\n" );
document.write( "            And indeed 30 + 60 = 90\r\n" );
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document.write( "Edwin

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