document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127562>Question 127562</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495188743/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 1 If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number.\r<BR>\n" );
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document.write( "2. The sum of a number an its reciprocal is 13/6. Find the numbers.\r<BR>\n" );
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document.write( "3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93517 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number.<BR>\n" );
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document.write( "Let the number to be added = x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%29%2F%28%282x%2B7%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%29%2F%28%282x%2B7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply, and solve for x <BR>\n" );
document.write( "4(2x+7) = 7(x+3)<BR>\n" );
document.write( "8x + 28 = 7x + 21<BR>\n" );
document.write( "8x - 7x = 21 - 28<BR>\n" );
document.write( "x = -7<BR>\n" );
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document.write( "Check solution in original equation, substitute -7 for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-7%2B3%29%29%2F%28%282%28-7%29%2B7%29%29 ALIGN=MIDDLE  ALT=\"%28%28-7%2B3%29%29%2F%28%282%28-7%29%2B7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F%28%28-14%2B7%29%29 ALIGN=MIDDLE  ALT=\"%28-4%29%2F%28%28-14%2B7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"%28-4%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F7 ALIGN=MIDDLE  ALT=\"4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >; minus into a minus is a plus<BR>\n" );
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document.write( ":\r<BR>\n" );
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document.write( "2. The sum of a number an its reciprocal is 13/6. Find the numbers.<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F6 ALIGN=MIDDLE  ALT=\"13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply equation by 6x to get rid of the denominators<BR>\n" );
document.write( "6x(x) + 6x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F6 ALIGN=MIDDLE  ALT=\"13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6x^2 + 6 = 13x<BR>\n" );
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document.write( "6x^2 - 13x + 6 = 0; a quadratic equation<BR>\n" );
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document.write( "After a little slogging, we find we can factor this to:<BR>\n" );
document.write( "(2x - 3)(3x - 2) = 0<BR>\n" );
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document.write( "2x = 3<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "3x = 2<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check solution using x = 3/2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F6 ALIGN=MIDDLE  ALT=\"13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F6 ALIGN=MIDDLE  ALT=\"9%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F6 ALIGN=MIDDLE  ALT=\"4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F6 ALIGN=MIDDLE  ALT=\"13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >; confirms our solution<BR>\n" );
document.write( "Note that the 2nd solution is the reciprocal of the 1st<BR>\n" );
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document.write( "3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool?<BR>\n" );
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document.write( "A typical shared work problem:<BR>\n" );
document.write( "Let t = time required when both pipes are open<BR>\n" );
document.write( "Let the full pool = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F5 ALIGN=MIDDLE  ALT=\"t%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F4 ALIGN=MIDDLE  ALT=\"t%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by a common multiple, 20 will work<BR>\n" );
document.write( "20*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F5 ALIGN=MIDDLE  ALT=\"t%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 20*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F4 ALIGN=MIDDLE  ALT=\"t%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20(1)<BR>\n" );
document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "4t + 5t = 20<BR>\n" );
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document.write( "9t = 20<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F9 ALIGN=MIDDLE  ALT=\"20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 2.22 hrs or 2 hrs & 13.3 min<BR>\n" );
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document.write( "Check solution using 2.22 for t:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.22%2F5 ALIGN=MIDDLE  ALT=\"2.22%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.22%2F4 ALIGN=MIDDLE  ALT=\"2.22%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ".444 + .555 = .999 ~ 1; confirms our solution<BR>\n" );
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document.write( "Could you follow the procedures in all these problems? Let me know if you have any questions <BR>\n" );
document.write( " </SPAN>\n" );
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