document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209274>Question 1209274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tractor has a rear wheel with a circumference of x m. The circumference of the front wheel is 5 m less. If the front wheel makes 15 more revolutions than the rear wheel every 450 m, what is the circumference, in m, of the front wheel?<BR>\n" );
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document.write( "Answer: <font color=red>10 meters</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "x = circumference of rear wheel<BR>\n" );
document.write( "x-5 = circumference of front wheel<BR>\n" );
document.write( "Each measurement is in meters. <BR>\n" );
document.write( "Each value is a positive real number.<BR>\n" );
document.write( "x-5 > 0 leads to x > 5<BR>\n" );
document.write( "So if any x value 5 or smaller shows up, we simply ignore it. <BR>\n" );
document.write( "The goal is to compute x-5.\r<BR>\n" );
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document.write( "One revolution of the rear wheel will mean that it travels x meters because it's the perimeter of the wheel.<BR>\n" );
document.write( "This assumes the wheel does <u>not</u> slip.\r<BR>\n" );
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document.write( "Two revolutions, the wheel travels 2x meters.<BR>\n" );
document.write( "Three revolutions, the wheel travels 3x meters.<BR>\n" );
document.write( "And so on.\r<BR>\n" );
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document.write( "After traveling 450 meters, the rear wheel makes 450/x revolutions. <BR>\n" );
document.write( "Meanwhile the front wheel makes 450/(x-5) revolutions which is 15 more compared to the previous amount.\r<BR>\n" );
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document.write( "(450/x) + 15 = 450/(x-5)<BR>\n" );
document.write( "x(x-5)*( (450/x) + 15 ) = x*(x-5)*( 450/(x-5) )<BR>\n" );
document.write( "450(x-5) + 15x(x-5) = 450x<BR>\n" );
document.write( "450x-2250 + 15x^2-75x = 450x<BR>\n" );
document.write( "450x-2250 + 15x^2-75x - 450x = 0<BR>\n" );
document.write( "15x^2 - 75x - 2250 = 0<BR>\n" );
document.write( "15(x^2 - 5x - 150) = 0<BR>\n" );
document.write( "x^2 - 5x - 150 = 0<BR>\n" );
document.write( "(x+10)(x-15) = 0<BR>\n" );
document.write( "x+10 = 0 or x-15 = 0<BR>\n" );
document.write( "x = -10 or x = 15<BR>\n" );
document.write( "Ignore the negative value since we stated earlier that x > 5.\r<BR>\n" );
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document.write( "If the real wheel has circumference x = 15 meters then it makes 450/x = 450/15 = 30 revolutions in the 450 meter distance.<BR>\n" );
document.write( "Meanwhile the front wheel makes 450/(x-5) = 450/(15-5) = 45 revolutions which is 15 more compared to the previous value.<BR>\n" );
document.write( "This helps verify we have the correct x value.\r<BR>\n" );
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document.write( "Then the last thing to do is compute x-5 to get x-5 = 15-5 = <font color=red>10 meters</font> as the circumference of the front wheel.<BR>\n" );
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