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\n" ); document.write( "The responses from the other two tutors both use formal algebraic methods to solve the problem, which is probably what the student was supposed to do.
\n" ); document.write( "However, solving the problem with formal algebra requires solving a quadratic equation using either difficult factoring or the quadratic formula.
\n" ); document.write( "So, if formal algebra is not required, the problem is solved much more quickly with a bit of estimation and mental arithmetic.
\n" ); document.write( "Note also that, even if a formal algebraic solution is required for the assignment, solving the problem with logical reasoning and mental arithmetic gives you valuable brain exercise.
\n" ); document.write( "It might go something like this.
\n" ); document.write( "For a very rough estimate, since the length is \"a bit more than 3 times the width\", let the width be x and the length be \"a bit more than 3x\", so that the area (length times width) is 1482.
\n" ); document.write( "1482 is a bit more than 3x^2
\n" ); document.write( "1482/3 = 496 is a bit more than x^2
\n" ); document.write( "The square root of 496 is a bit more than 22; so the width should be either 22 or perhaps 21.
\n" ); document.write( "Then mental arithmetic determines that 21 is a factor of 1428 while 22 is not, so the width is probably 21.
\n" ); document.write( "Dividing 1428 by 21 gives 68; and 68 is 5 more than 3 times 21. So we have the answer.
\n" ); document.write( "ANSWERS: width 21, length 68
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