document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274883>Question 274883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My son has 2 problems.<BR>\n" );
document.write( "(1) A boy is mowing a field 40 rods and 20 rods rectangular.  How wide a border must he cut in order that 3/4 of the mowing will have been completed?\r<BR>\n" );
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document.write( "(2) Solve for x and y.  3X + 8y=-5 and x^2- 2XY=12.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200591 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=200591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) A boy is mowing a field 40 rods and 20 rods rectangular.<BR>\n" );
document.write( " How wide a border must he cut in order that 3/4 of the mowing will have been completed?<BR>\n" );
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document.write( "Find the area of the field, 40 * 20 = 800 sq/rds<BR>\n" );
document.write( "Mowed area has to equal .75(800) = 600 sq/rds<BR>\n" );
document.write( "That leaves 200 sq/rds unmowed<BR>\n" );
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document.write( "let x = the width of the swath around the unmowed area<BR>\n" );
document.write( "unmowed length * unmowed width = 200 sq/rd<BR>\n" );
document.write( "(40-2x)*(20-2x) = 200<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "800 - 80x - 40x + 4x^2 = 200<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "4x^2 - 120x + 800 - 200 = 0<BR>\n" );
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document.write( "4x^2 - 120x + 600 = 0<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "x^2 - 30x + 150 = 0<BR>\n" );
document.write( "Use the quadratic formula to solve for x, (only one solution will make sense)<BR>\n" );
document.write( "a=1, b=-30, c=150<BR>\n" );
document.write( "I got x ~ 6.34 rods is the width to mowed<BR>\n" );
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document.write( "(2) Solve for x and y. <BR>\n" );
document.write( "3X + 8y =-5 and x^2- 2XY = 12. <BR>\n" );
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document.write( "try to get the 2nd equation in a form where we can eliminate y<BR>\n" );
document.write( "x^2 - 2xy = 12<BR>\n" );
document.write( "x(x - 2y) = 12<BR>\n" );
document.write( "x - 2y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fx ALIGN=MIDDLE  ALT=\"12%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by 4 and add the 1st equation<BR>\n" );
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document.write( "3x + 8y = -5<BR>\n" );
document.write( "4x - 8y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fx ALIGN=MIDDLE  ALT=\"48%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------- eliminates y, find x<BR>\n" );
document.write( "7x + 0y = -5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fx ALIGN=MIDDLE  ALT=\"48%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7x + 5 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fx ALIGN=MIDDLE  ALT=\"48%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "multiply by x<BR>\n" );
document.write( "7x^2 + 5x - 48 = 0; hopefully an equation we can factor<BR>\n" );
document.write( "(7x-16)(x+3) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "7x = 16<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "Use the integer solution in the 1st equation to find y<BR>\n" );
document.write( "3x + 8y = -5<BR>\n" );
document.write( "3(-3) + 8y = -5<BR>\n" );
document.write( "-9 + 8y = -5<BR>\n" );
document.write( "8y = -5 + 9<BR>\n" );
document.write( "8y = +4<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F8 ALIGN=MIDDLE  ALT=\"4%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = +.5<BR>\n" );
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document.write( "Our solution: x=-3; y=+.5<BR>\n" );
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document.write( "See if that works in the 2nd equation<BR>\n" );
document.write( "x^2- 2XY = 12. <BR>\n" );
document.write( "-3^2 - 2*-3*.5 = 12<BR>\n" );
document.write( "9 - (-3) = 12<BR>\n" );
document.write( "9 + 3 = 12; so it works, the value x = 16/7 may work too, but you can check that out yourself\r<BR>\n" );
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