document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=657207>Question 657207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> will you please help me solve this problem, I am not even sure how to start working it out, i cant even figure how to write an equation for this problem. please help: \"the sum of 8 times Sara's age and 5 times Ashley's age is 81. Ashley's is 9 years less than twice Sara's age. Find the age of each girl.\"<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #409794 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=409794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Divide and conquer. Working one piece of the problem at a time, you need to read, interpret, and write as equations the pieces of information given.<BR>\n" );
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document.write( "I would start by defining a variable, like this:<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be Sara's age (in years, of course).<BR>\n" );
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document.write( "\"Ashley's is 9 years less than twice Sara's age.\"<BR>\n" );
document.write( "Twice Sara's age would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and 9 years less than that<BR>\n" );
document.write( "would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9 ALIGN=MIDDLE  ALT=\"2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, Ashley's age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9 ALIGN=MIDDLE  ALT=\"2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "\"The sum of 8 times Sara's age and 5 times Ashley's age\" involves<BR>\n" );
document.write( "8 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x ALIGN=MIDDLE  ALT=\"8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "5 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9 ALIGN=MIDDLE  ALT=\"2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%282x-9%29 ALIGN=MIDDLE  ALT=\"5%282x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The sum of those two numbers is 81, which means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288x%2B5%282x-9%29=81%29 ALIGN=MIDDLE  ALT=\"highlight%288x%2B5%282x-9%29=81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That is your equation.<BR>\n" );
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document.write( "Now, we solve:<BR>\n" );
document.write( "First, we simplify the equation a bit.<BR>\n" );
document.write( "To get rid of a parenthesis that is multiplied by a number (or an expression), we use the distributive property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B5%282x-9%29=81 ALIGN=MIDDLE  ALT=\"8x%2B5%282x-9%29=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B5%2A%282x%29%2B5%2A%28-9%29=81 ALIGN=MIDDLE  ALT=\"8x%2B5%2A%282x%29%2B5%2A%28-9%29=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B10x-45=81 ALIGN=MIDDLE  ALT=\"8x%2B10x-45=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-45=81 ALIGN=MIDDLE  ALT=\"18x-45=81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From there, we solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-45=81 ALIGN=MIDDLE  ALT=\"18x-45=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-45%2B45=81%2B45 ALIGN=MIDDLE  ALT=\"18x-45%2B45=81%2B45\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x=126 ALIGN=MIDDLE  ALT=\"18x=126\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding 45 to both sides of the equal sign)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x=126 ALIGN=MIDDLE  ALT=\"18x=126\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2F18=126%2F18 ALIGN=MIDDLE  ALT=\"18x%2F18=126%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=7%29 ALIGN=MIDDLE  ALT=\"highlight%28x=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (dividing both sides by 18)<BR>\n" );
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document.write( "Now we can translate the algebra back into words.<BR>\n" );
document.write( "Sara is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287%29 ALIGN=MIDDLE  ALT=\"highlight%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We said above that Ashley's age was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9 ALIGN=MIDDLE  ALT=\"2x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "Ashley's age is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A7-9=highlight%285%29 ALIGN=MIDDLE  ALT=\"2%2A7-9=highlight%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The sum of 8 times Sara's age and 5 times Ashley's age is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2B5%2A5=56%2B25 ALIGN=MIDDLE  ALT=\"8%2A7%2B5%2A5=56%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56%2B25=81 ALIGN=MIDDLE  ALT=\"56%2B25=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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