document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122228>Question 122228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)If 3 is subtracted from the numerator of a certain fraction,the value of the fraction becomes 3/5.If 1 is subtracted from the denominator of the same fraction,it becomes 2/3.Find the original fraction.\r<BR>\n" );
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document.write( "2)Find the product of 2 numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second.\r<BR>\n" );
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document.write( "3)The second  of the four numbers is three less than the first,the third is four more than the first and the fourth is two more than the third.Find the fourth number if the sum is 35. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89864 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=89864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)If 3 is subtracted from the numerator of a certain fraction,the value of the fraction becomes 3/5.If 1 is subtracted from the denominator of the same fraction,it becomes 2/3.Find the original fraction.<BR>\n" );
document.write( "Let the \"certain fraction\" = <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;\" ><BR>\n" );
document.write( "If 3 is subtracted from the numerator, the value is 3/5. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28x-3%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply:<BR>\n" );
document.write( "5(x-3) = 3y<BR>\n" );
document.write( "5x - 15 = 3y<BR>\n" );
document.write( "5x - 3y = 15; eq1<BR>\n" );
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document.write( "If 1 is subtracted from the denominator of the same fraction,it becomes 2/3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28y-1%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28y-1%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( "3x = 2(y-1)<BR>\n" );
document.write( "3x = 2y - 2<BR>\n" );
document.write( "3x - 2y = -2;eq2<BR>\n" );
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document.write( "We're going to use elimination: mult eq1 by 2 and eq2 by 3:<BR>\n" );
document.write( "10x - 6y = 30<BR>\n" );
document.write( " 9x - 6y = -6<BR>\n" );
document.write( "------------------subtracting eliminates y; find x<BR>\n" );
document.write( "1x = 36 is the numerator<BR>\n" );
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document.write( "Find y using: 5x - 3y = 15<BR>\n" );
document.write( "5(36) - 3y = 15<BR>\n" );
document.write( "180 - 3y = 15<BR>\n" );
document.write( "-3y = 15 - 180<BR>\n" );
document.write( "-3y = -165<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-165%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"%28-165%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 55 is the denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F55 ALIGN=MIDDLE  ALT=\"36%2F55\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our certain fraction<BR>\n" );
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document.write( "You can check the solutions by substitution<BR>\n" );
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document.write( "2)Find the product of 2 numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second.<BR>\n" );
document.write( "Let the two numbers = x & y; find the two numbers, then worry about the product<BR>\n" );
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document.write( "twice the first added to the second equals 19<BR>\n" );
document.write( "2x + y = 19<BR>\n" );
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document.write( "3 times the first is 21 more than the second<BR>\n" );
document.write( "3x = y + 21<BR>\n" );
document.write( "3x - y = 21<BR>\n" );
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document.write( "add the two equations<BR>\n" );
document.write( "2x + y = 19<BR>\n" );
document.write( "3x - y = 21<BR>\n" );
document.write( "-------------adding eliminates y, find x<BR>\n" );
document.write( "5x = 40<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F5 ALIGN=MIDDLE  ALT=\"40%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 8<BR>\n" );
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document.write( "Find y using 2x + y = 19<BR>\n" );
document.write( "2(8) + y = 19<BR>\n" );
document.write( "y = 19 - 16<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "Obviously the product is 8 * 3 = 24<BR>\n" );
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document.write( "Check solutions in 3x - y = 21<BR>\n" );
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document.write( "3)The second of the four numbers is three less than the first,the third is four more than the first and the fourth is two more than the third.Find the fourth number if the sum is 35.<BR>\n" );
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document.write( "Let our 4 numbers be = to 35 as it says.<BR>\n" );
document.write( "w + x + y + z = 35<BR>\n" );
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document.write( "The second of the four numbers is 3 less than the first:<BR>\n" );
document.write( "x = (w-3)<BR>\n" );
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document.write( "the third is 4 more than the first<BR>\n" );
document.write( "y = (w+4)<BR>\n" );
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document.write( "the fourth is two more than the third<BR>\n" );
document.write( "z = (y+2)<BR>\n" );
document.write( "we want all the variables in terms of w, substitute (w+4) for y<BR>\n" );
document.write( "z = (w+4) + 2<BR>\n" );
document.write( "z = (w+6)<BR>\n" );
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document.write( "Substitute for x, y & z in the total equation<BR>\n" );
document.write( "w + (w-3) + (w+4) + (w+6) = 35<BR>\n" );
document.write( "4w - 3 + 4 + 6 = 35<BR>\n" );
document.write( "4w + 7 = 35<BR>\n" );
document.write( "4w = 35 - 7<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2F4 ALIGN=MIDDLE  ALT=\"28%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = 7<BR>\n" );
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document.write( "The want the 4th number (z)<BR>\n" );
document.write( "z = 7 + 6<BR>\n" );
document.write( "z = 13<BR>\n" );
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document.write( "Check solutions by substitution, see if I'm right </SPAN>\n" );
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