document.write( "Question 1181290: A mathematics teacher prepared a test consisting of 50 problems worth 2 points, 5 points, and 10 points each. If the number of 2-point problems is thrice the number of 10-point problems, and the number of 5-point problems is 10 less than twice the number of 2-point problems, how many points is the entire test? \n" ); document.write( "

Algebra.Com's Answer #811172 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "A mathematics teacher prepared a test consisting of 50 problems worth 2 points, 5 points, and 10 points each.
\n" ); document.write( "If the number of 2-point problems is thrice the number of 10-point problems,
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\n" ); document.write( "how many points is the entire test?
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document.write( "Let x be the number of the 10-point problems.\r\n" );
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document.write( "Then the number of the 2-point problems is 3x, according to the condition,\r\n" );
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document.write( "and the number of the 5-point problems is  (2*(3x) - 10) = (6x-10).\r\n" );
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document.write( "Now we write an equation for the total number of problems\r\n" );
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document.write( "    x + 3x + (6x-10) = 50   problems.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    x + 3x + 6x = 50 + 10\r\n" );
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document.write( "        10x     = 60\r\n" );
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document.write( "          x     = 60/10 = 6.\r\n" );
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document.write( "So, the number of the 10-point problems is 6;\r\n" );
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document.write( "    the number of the  2-point problems is 3*6 = 18,\r\n" );
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document.write( "    and of the 5-point problems is (6x-10) = 6*6-10 = 26.\r\n" );
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document.write( "As a check,  6 + 18 + 26 = 50 problems, in all.\r\n" );
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document.write( "Now the last step of the solution is to calculate the number of points.  It is\r\n" );
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document.write( "    6*10 + 18*2 + 26*5 = 226.\r\n" );
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document.write( "ANSWER.  The entire test is 226 points.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Couple of post-notes.\r
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document.write( "    From the first glance, this problem is for 3 unknowns and 3 equations.\r\n" );
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document.write( "    But it is not so.\r\n" );
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document.write( "    It easily can be solved using one single equation in one single unknown.\r\n" );
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document.write( "    Moreover, this problem and many other similar problems, are DESIGNED, are INTENDED\r\n" );
document.write( "        and are EXPECTED to be solved PRECISELY in this way.\r\n" );
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document.write( "    Solving such problems in this way has important educational goal \r\n" );
document.write( "    to train and to prepare a mathematically literate student.\r\n" );
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