Algebra.Com's Answer #797826 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A quantity y partly varies directly as x and partly varies inversely as x when x = 4, y = 17.
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document.write( "When x = 6, y = 13 , find the value of y when x = 10.
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document.write( " This formulation is terrible.\r
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document.write( " This problem uses forms of the language that go, probably, from Middle Ages.\r
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document.write( " It costed me huge efforts to guess what does it mean.\r
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document.write( " I do not think that an average modern/contemporary student can understand this language and the meaning.\r
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document.write( " Nevertheless . . . \r
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document.write( "The problem means that y is this function y = ax +  with unknown coefficient \"a\" and \"b\".\r\n" );
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document.write( "To find these coefficients, we have these equations from the condition\r\n" );
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document.write( " x= 4 : 4a +  = 17 (1)\r\n" );
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document.write( " x = 6 : 6a +  = 13 (2)\r\n" );
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document.write( "To solve this system, multiply equation (1) by 4 (both sides); multiply equation (2) by 6 (both sides).\r\n" );
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document.write( "You will get\r\n" );
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document.write( " 16a + b = 68 (3)\r\n" );
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document.write( " 36a + b = 78 (4)\r\n" );
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document.write( "Subtract equation (3) from equation (4) to eliminate \"b\" and to get \"a\" :\r\n" );
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document.write( " 36a - 16a = 78 - 68\r\n" );
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document.write( " 20a = 10\r\n" );
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document.write( " a = 10/20 = 0.5.\r\n" );
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document.write( "Then from (3),\r\n" );
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document.write( " 16*0.5 + b = 68,\r\n" );
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document.write( " b = 68 - 8 = 60.\r\n" );
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document.write( "Thus the function y is y = 0.5x +  .\r\n" );
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document.write( "Hence, at x= 10, y = 0.5*10 +  = 5 + 6 = 11. ANSWER\r\n" );
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document.write( "Solved.\r
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