document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91669>Question 91669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #1  Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second.\r<BR>\n" );
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document.write( "#2   An airplane covered 13 miles of its route while decreasing its altitude by 44,000 feet.  Find the slope of the airplane's line of descent.  Round to the nearest hundredth.  [Hint: 1 mi = 5280 feet.]<BR>\n" );
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document.write( "#3   The difference of two positive numbers is 39.  The larger number is 9 less than 4 times the smaller number.  What are the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66571 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=66571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1 Find two consecutive odd integers <BR>\n" );
document.write( "x, (x+2)<BR>\n" );
document.write( "such that 5 times the first integer is 12 more than 3 times the second.<BR>\n" );
document.write( "5x = 3(x+2) + 12<BR>\n" );
document.write( "5x = 3x + 6 + 12<BR>\n" );
document.write( "5x - 3x = 18<BR>\n" );
document.write( "2x = 18<BR>\n" );
document.write( "x = 18/2<BR>\n" );
document.write( "x = 9 and 11 are two odd consecutive integers. <BR>\n" );
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document.write( "5(9) = 3(11) + 12<BR>\n" );
document.write( "45 = 33 + 12<BR>\n" );
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document.write( "#2 An airplane covered 13 miles of its route while decreasing its altitude by 44,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.]<BR>\n" );
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document.write( "One of the definitions of slope is \"rise over run\", a decrease in altitude would<BR>\n" );
document.write( "be a negative rise, so we have altitude change/horizontal change.<BR>\n" );
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document.write( "Change feet to miles: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44000%2F5280 ALIGN=MIDDLE  ALT=\"44000%2F5280\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8.33 mi<BR>\n" );
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document.write( "Slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8.33%2F13 ALIGN=MIDDLE  ALT=\"-8.33%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.64<BR>\n" );
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document.write( "You could do it with feet too,<BR>\n" );
document.write( "Slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-44000%2F%28%2813%2A5280%29%29 ALIGN=MIDDLE  ALT=\"-44000%2F%28%2813%2A5280%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.64<BR>\n" );
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document.write( "#3 The difference of two positive numbers is 39.<BR>\n" );
document.write( "x - y = 39<BR>\n" );
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document.write( "-y  = 39 - x<BR>\n" );
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document.write( "+y = (x - 39); use for substitution<BR>\n" );
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document.write( "The larger number is 9 less than 4 times the smaller number.<BR>\n" );
document.write( "x = 4y - 9<BR>\n" );
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document.write( "What are the two numbers?<BR>\n" );
document.write( "Substitute (x-39) for y in the above equation:<BR>\n" );
document.write( "4(x-39) - 9 = x<BR>\n" );
document.write( "4x - 156 -9 = x<BR>\n" );
document.write( "4x - 165 = x<BR>\n" );
document.write( "4x - x = +165<BR>\n" );
document.write( "3x = 165<BR>\n" );
document.write( "x = 165/3<BR>\n" );
document.write( "x = 55<BR>\n" );
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document.write( "Find y: y = 55-39 = 16<BR>\n" );
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document.write( "Check solution in x = 4y - 9<BR>\n" );
document.write( "55 = 4(16) - 9<BR>\n" );
document.write( "55 = 64 - 9<BR>\n" );
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document.write( "Did you understand what we did here? </SPAN>\n" );
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