document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320596>Question 320596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of a gear varies directly as the number of teeth it contains. If a gear with 10 teeth rotates at 240rpm, with what speed would a gear with 18 teeth revolve under the same conditions? \r<BR>\n" );
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document.write( "I'm getting 2 answers not sure which one is right 240x10=2400/18=133<BR>\n" );
document.write( "240x18=4320/10=432 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229598 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = # of teeth and y = rpm\r<BR>\n" );
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document.write( "So \"If a gear with 10 teeth rotates at 240rpm\", then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=240 ALIGN=MIDDLE  ALT=\"y=240\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Because \"The speed of a gear varies directly as the number of teeth it contains\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=kx ALIGN=MIDDLE  ALT=\"y=kx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=240 ALIGN=MIDDLE  ALT=\"y=240\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=k%2810%29 ALIGN=MIDDLE  ALT=\"240=k%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for 'k' to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=240%2F10=24 ALIGN=MIDDLE  ALT=\"k=240%2F10=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=24 ALIGN=MIDDLE  ALT=\"k=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > giving us the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24x ALIGN=MIDDLE  ALT=\"y=24x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we want to know the rpm when 18 teeth are involved. So now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=18 ALIGN=MIDDLE  ALT=\"x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug this into the equation above to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24%2818%29=432 ALIGN=MIDDLE  ALT=\"y=24%2818%29=432\"   DISABLED_style= \"max-width:90%; height:auto;\" > meaning that a 18 tooth gear will spin at 432 rpm. \r<BR>\n" );
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document.write( "Alternate Solution:\r<BR>\n" );
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document.write( "\"If a gear with 10 teeth rotates at 240rpm, with what speed would a gear with 18 teeth revolve under the same conditions? \" means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F240=18%2Fx ALIGN=MIDDLE  ALT=\"10%2F240=18%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Basically, the ratio of the number of teeth to the rpm is the same. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F240=18%2Fx ALIGN=MIDDLE  ALT=\"10%2F240=18%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given ratio\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F240%29%2Ax=18 ALIGN=MIDDLE  ALT=\"%2810%2F240%29%2Ax=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax=18%2A240 ALIGN=MIDDLE  ALT=\"10%2Ax=18%2A240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 240\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax=4320 ALIGN=MIDDLE  ALT=\"10%2Ax=4320\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4320%2F10 ALIGN=MIDDLE  ALT=\"x=4320%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=432 ALIGN=MIDDLE  ALT=\"x=432\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So our answer is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=432 ALIGN=MIDDLE  ALT=\"x=432\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that a gear with 18 teeth will rotate at 432 rpm. So we get the same answer.\r<BR>\n" );
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