document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149008>Question 149008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The ratio of two numbers in 6:1.If their difference is 35, what is the smaller number?<BR>\n" );
document.write( "2. The ratio of the width to the length of a rectangle is 2:3. If the area of the rectanglle is 216 sq. cm. , what is its width?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109357 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=109357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The ratio of two numbers in 6:1.If their difference is 35, what is the smaller number?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x= a number; y = smaller number<BR>\n" );
document.write( "Write an equation for each statement<BR>\n" );
document.write( "\"The ratio of two numbers in 6:1\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy ALIGN=MIDDLE  ALT=\"x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F1 ALIGN=MIDDLE  ALT=\"6%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If their difference is 35,\"<BR>\n" );
document.write( "x - y = 35<BR>\n" );
document.write( "x = y + 35<BR>\n" );
document.write( ":<BR>\n" );
document.write( "what is the smaller number?<BR>\n" );
document.write( "Substitute (y+35) for x in the ratio equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B35%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28y%2B35%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F1 ALIGN=MIDDLE  ALT=\"6%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "y + 35 = 6y<BR>\n" );
document.write( "35 = 6y - y<BR>\n" );
document.write( "35 = 5y<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F5 ALIGN=MIDDLE  ALT=\"35%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 7 is the smaller number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check: larger number would be 7 + 35 = 42, we can see that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F7 ALIGN=MIDDLE  ALT=\"42%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F1 ALIGN=MIDDLE  ALT=\"6%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2. The ratio of the width to the length of a rectangle is 2:3. If the area of the rectangle is 216 sq. cm. , what is its width? <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2FL ALIGN=MIDDLE  ALT=\"W%2FL\"   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;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "L * W = 216<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216%2FW ALIGN=MIDDLE  ALT=\"216%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute (216/W) for L in the ratio equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%2F%28%28216%2FW%29%29 ALIGN=MIDDLE  ALT=\"W%2F%28%28216%2FW%29%29\"   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;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "3W = 2*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216%2FW ALIGN=MIDDLE  ALT=\"216%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3W = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2FW ALIGN=MIDDLE  ALT=\"432%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by W, get rid of the denominator and you have:<BR>\n" );
document.write( "3W^2 = 432<BR>\n" );
document.write( ":<BR>\n" );
document.write( "W^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2F3 ALIGN=MIDDLE  ALT=\"432%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "W^2 = 144<BR>\n" );
document.write( "W = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the square root of both sides<BR>\n" );
document.write( "W = 12 cm is the width<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution<BR>\n" );
document.write( "L = 216/12 = 18 cm<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F18 ALIGN=MIDDLE  ALT=\"12%2F18\"   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;\" > confirms our solution<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did this make sense to you? Any questions? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );