document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149189>Question 149189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, can you please help me solve this problems:<BR>\n" );
document.write( "1.)  One number is 3 more than the other. Their sum is 7. Find the numbers.\r<BR>\n" );
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document.write( "2.)  The denominator of a fraction is twice the numerator. If the sum of the<BR>\n" );
document.write( "     terms is 3, what is the fraction?\r<BR>\n" );
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document.write( "3.)  The sum of two numbers is 165 and their difference is 29. Find the<BR>\n" );
document.write( "     numbers. \r<BR>\n" );
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document.write( "4.)  If the numerator of a certain fraction is increased by 6 and its <BR>\n" );
document.write( "     denominator is decreased by 5, the resulting fraction is equal to 3/4.<BR>\n" );
document.write( "     If the reciprocal of the original fraction is decreased by 1, the <BR>\n" );
document.write( "     resulting fraction is 16/9. Find the original fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109495 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=109495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) One number is 3 more than the other. Their sum is 7. Find the numbers.<BR>\n" );
document.write( "Let x = \"one number<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-3) = \"other number<BR>\n" );
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document.write( "\"Their sum is 7\"<BR>\n" );
document.write( "x + (x-3) = 7<BR>\n" );
document.write( "2x = 7 + 3<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F2 ALIGN=MIDDLE  ALT=\"10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 5<BR>\n" );
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document.write( "Check: 5 - 3 = 2: 5 + 2 = 7<BR>\n" );
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document.write( "2.) The denominator of a fraction is twice the numerator. If the sum of the<BR>\n" );
document.write( "terms is 3, what is the fraction?<BR>\n" );
document.write( "Let x = the numerator<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2x = denominator<BR>\n" );
document.write( "Obviously, if x + 2x = 3, then x = 1 and the fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "3.) The sum of two numbers is 165 and their difference is 29. Find the<BR>\n" );
document.write( "numbers.<BR>\n" );
document.write( "x + y = 165 <BR>\n" );
document.write( "x - y = 29<BR>\n" );
document.write( "------------adding eliminates y:<BR>\n" );
document.write( "2x + 0 = 194<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=194%2F2 ALIGN=MIDDLE  ALT=\"194%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 97<BR>\n" );
document.write( "I'll let you find y<BR>\n" );
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document.write( "4.) If the numerator of a certain fraction is increased by 6 and its<BR>\n" );
document.write( "denominator is decreased by 5, the resulting fraction is equal to 3/4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B6%29%29%2F%28%28d-5%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B6%29%29%2F%28%28d-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "If the reciprocal of the original fraction is decreased by 1, the<BR>\n" );
document.write( "resulting fraction is 16/9.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fn ALIGN=MIDDLE  ALT=\"d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F9 ALIGN=MIDDLE  ALT=\"16%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fn ALIGN=MIDDLE  ALT=\"d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F9 ALIGN=MIDDLE  ALT=\"16%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fn ALIGN=MIDDLE  ALT=\"d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F9 ALIGN=MIDDLE  ALT=\"16%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F9 ALIGN=MIDDLE  ALT=\"9%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fn ALIGN=MIDDLE  ALT=\"d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F9 ALIGN=MIDDLE  ALT=\"25%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Find the original fraction.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F25 ALIGN=MIDDLE  ALT=\"9%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check solution in the 1st statement:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B6%29%29%2F%28%28d-5%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B6%29%29%2F%28%28d-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289%2B6%29%29%2F%28%2825-5%29%29 ALIGN=MIDDLE  ALT=\"%28%289%2B6%29%29%2F%28%2825-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F20 ALIGN=MIDDLE  ALT=\"15%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; confirms our solutions<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );