document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595566>Question 595566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1) The sum of three consecutive odd integers is 117. Find the integers.<BR>\n" );
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document.write( "(2) Long distance carrier A charges $12.95 per month and $0.07 per minute for international calls to greece, and long distance carrier B charges $3.95 per month and $0.12 per minute. For how many minutes will the monthly cost be the same? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377208 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there--<BR>\n" );
document.write( "(1) The sum of three consecutive odd integers is 117. Find the integers.\r<BR>\n" );
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document.write( "Let x be the first integer. Then x+1 is the second integer, and x+2 is the third integer. The sum of the integers is 117, so we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bx%2B1%2Bx%2B2=117 ALIGN=MIDDLE  ALT=\"x%2Bx%2B1%2Bx%2B2=117\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3=117 ALIGN=MIDDLE  ALT=\"3x%2B3=117\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=114 ALIGN=MIDDLE  ALT=\"3x=114\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=38 ALIGN=MIDDLE  ALT=\"x=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The three integers are 38, 39, and 40. Check to make sure: 38+39+40=117. Bingo!<BR>\n" );
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document.write( "(2) Long distance carrier A charges $12.95 per month and $0.07 per minute for international calls to greece, and long distance carrier B charges $3.95 per month and $0.12 per minute. For how many minutes will the monthly cost be the same?<BR>\n" );
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document.write( "The first step in this problem is to write equations to model each long distance plan. Let m be the number of minutes and C be the monthly cost.<BR>\n" );
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document.write( "Carrier A: a flat fee of $12.95 plus $0.07 per minute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12.95%2B0.07m ALIGN=MIDDLE  ALT=\"C=12.95%2B0.07m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Carrier B: flat fee of $3.95 plus $0.12 per minute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3.95%2B0.12m ALIGN=MIDDLE  ALT=\"C=3.95%2B0.12m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We want to know the number of minutes for which the two plans have the same cost. So, let's assume that the costs are the same and figure out what m would have to be in order to make that true. Algebraically, we have two expressions for C, so we set them equal to each other. (Lots of students get stuck at this point. Keep reading, but if you still don't understand, send me an email and I'll explain in more detail.)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.95%2B0.07m=3.95%2B0.12m ALIGN=MIDDLE  ALT=\"12.95%2B0.07m=3.95%2B0.12m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we just simplify and solve for m. Combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.00=0.05m ALIGN=MIDDLE  ALT=\"9.00=0.05m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 0.05<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=m ALIGN=MIDDLE  ALT=\"180=m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So 180 minutes of long distance calling costs the same in either plan. Let's check and see if that's really true. Substitute 180 for m in each equation.<BR>\n" );
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document.write( "Carrier A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12.95%2B0.07m ALIGN=MIDDLE  ALT=\"C=12.95%2B0.07m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12.95%2B%280.07%29%28180%29 ALIGN=MIDDLE  ALT=\"C=12.95%2B%280.07%29%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=12.95%2B12.60 ALIGN=MIDDLE  ALT=\"C=12.95%2B12.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=25.55 ALIGN=MIDDLE  ALT=\"C=25.55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Carrier B:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3.95%2B0.12m ALIGN=MIDDLE  ALT=\"C=3.95%2B0.12m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3.95%2B%280.12%29%28180%29 ALIGN=MIDDLE  ALT=\"C=3.95%2B%280.12%29%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3.95%2B21.60 ALIGN=MIDDLE  ALT=\"C=3.95%2B21.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=25.55 ALIGN=MIDDLE  ALT=\"C=25.55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We see that it is true; when you use 180 minutes, both plans cost $25.55.<BR>\n" );
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document.write( "Hope that helps! Email if you have questions.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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