document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276564>Question 276564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lens equation for a camera is 1/f= 1/di+1/d0, where f is the focal length of the lens, di is the distance between the lens and the film, and d0 is the distance between the lens and the object. For a certain camera, an object that is 18 cm from the lens is in focus when the lens is 9 cm from the film. What is the focal length of the lens?  \r<BR>\n" );
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document.write( "this is what i worked it out too-> 1/f= 4/9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201683 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=201683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff=+1%2Fd%5Bi%5D+%2B+1%2Fd%5Bo%5D ALIGN=MIDDLE  ALT=\"1%2Ff=+1%2Fd%5Bi%5D+%2B+1%2Fd%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are given that the distance from the lens to the object, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bo%5D ALIGN=MIDDLE  ALT=\"d%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is 18 and the the distance from the lens to the film, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bi%5D ALIGN=MIDDLE  ALT=\"d%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is 9. Substituting these into the equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff=+1%2F18+%2B+1%2F9 ALIGN=MIDDLE  ALT=\"1%2Ff=+1%2F18+%2B+1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are several ways to solve for f:<ul><li>Add the fractions on the right and then ...<ul><li>solve the resulting proportion; or</li><li>flip both sides upside down. (Flipping equations upside down is not genuine Math. But in this case it works. This is so because the left side represents the reciprocal of f. So when we add the fractions on the right we will have a fraction that represents the reciprocal of f. And the reciprocal of a reciprocal is the original number, This is why we can flip the fractions on each side upside down <b>after you have added the fractions, not before. </b></li></ul></li><li>Eliminate the fractions entirely by multiplying both sides by the Lowest Common Denominator (LCD) of all three fractions and the solve the resulting fraction-less equation.</li></ul><BR>\n" );
document.write( "I am going to use the last method. The LCD of all three fractions is 18f. So multiply both sides by 18f:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18f%281%2Ff%29+=+18f%281%2F18+%2B+1%2F9%29 ALIGN=MIDDLE  ALT=\"18f%281%2Ff%29+=+18f%281%2F18+%2B+1%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the right side we need to use the Distributive Property to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18f%281%2Ff%29+=+18f%281%2F18%29+%2B+18f%281%2F9%29 ALIGN=MIDDLE  ALT=\"18f%281%2Ff%29+=+18f%281%2F18%29+%2B+18f%281%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In each term the denominator cancels:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18cross%28f%29%281%2Fcross%28f%29%29+=+cross%2818%29f%281%2Fcross%2818%29%29+%2B+cross%289%29%2A2%2Af%281%2Fcross%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+f+%2B+2f ALIGN=MIDDLE  ALT=\"18+=+f+%2B+2f\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify the right side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+=+3f ALIGN=MIDDLE  ALT=\"18+=+3f\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by 3 we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+f ALIGN=MIDDLE  ALT=\"6+=+f\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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