document.write( "Question 1208603: 14 is added to 2\3 of a number. The result is 1 whole number 1\4 times the original number.find the numbers. \n" ); document.write( "

Algebra.Com's Answer #846968 by Edwin McCravy(20060) $\"\"$ $\"About$

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14 is added to 2\3 of a number. The result is 1 whole number 1\4 times the
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document.write( "That is not grammatical. Something is wrong or missing.\r\n" );
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document.write( "Tutor Ikleyn assumed \"1 whole number 1\4\" meant \"1 PLUS 1/4\" or 5/4.\r\n" );
document.write( "IOW, she interpreted it to mean this:\r\n" );
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document.write( "14 is added to 2/3 of a number. The result is  times the original number. Find the number.\r\n" );
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document.write( "With her interpretation, she obtained the answer as 24.\r\n" );
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document.write( "Notice that the student wrote \"find the numbers\" (plural) but she \r\n" );
document.write( "only found only one number, and changed \"numbers\" to \"number\".\r\n" );
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document.write( "Tutor josgarithmetic(39489) interpreted it as though the \"1\4 times\" was\r\n" );
document.write( "reversed and should be \"times 1/4\".  He interpreted it as:\r\n" );
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document.write( "14 is added to 2/3 of a number. The result is 1 whole number times 1/4 the\r\n" );
document.write( "original number. Find the numbers.  \r\n" );
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document.write( "He gave an example where the original number is -84 and the whole number is 2.\r\n" );
document.write( "There are 6 solutions in all for his interpretation:\r\n" );
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document.write( "(-84,2), (-21,0), (6,12), (24,5), (42,4), (168,3)\r\n" );
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document.write( "I will assume that the student inadvertently omitted the word PLUS.\r\n" );
document.write( "So I'll do it with this interpretation:\r\n" );
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document.write( "14 is added to 2/3 of a number. The result is 1 whole number PLUS 1/4 times\r\n" );
document.write( "the original number. Find the numbers.\r\n" );
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document.write( "Let x be the original number and let y be the 1 whole number.\r\n" );
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document.write( "Solve for y, which must be a whole number:\r\n" );
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document.write( "Since y must be a whole number, x must be a multiple of 12\r\n" );
document.write( "to cancel the denominator in the first term.\r\n" );
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document.write( "Let x = 12k\r\n" );
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document.write( "Whole numbers are non-negative integers, so\r\n" );
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document.write( "k is an integer, so \r\n" );
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document.write( "So the infinite set of solutions is \r\n" );
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document.write( "{ (12k, 5k+14) | k > -2 }.\r\n" );
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document.write( "Some examples of solutions are:\r\n" );
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document.write( "(-24,4), (-12,9), (0,14), (12,19), (24,24), (36,29), (48,34), ...\r\n" );
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document.write( "Edwin

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