document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192566>Question 192566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Practical Application of Quadratic Equations \r<BR>\n" );
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document.write( "1.A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet? <BR>\n" );
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document.write( "2.A business invests $8,000 in a savings account for two years.  At the beginning of the second year, an additional $2,500 is invested.  At the end of the second year, the account balance is $11,445.  What was the annual interest rate? \r<BR>\n" );
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document.write( "3.Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. <BR>\n" );
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document.write( "           4. The Hudson River flows at a rate of 5 miles per hour.  A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours.  What is the speed of the boat in still water?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144612 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=144612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?<BR>\n" );
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document.write( "Let x = the width of the path<BR>\n" );
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document.write( "(2x+15) by (2x+11) = overall area of the garden and the path<BR>\n" );
document.write( "and FOIL this<BR>\n" );
document.write( "Overall Area = 4x^2 + 52x + 165<BR>\n" );
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document.write( "Garden area: 15 * 11 = 165 <BR>\n" );
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document.write( "Overall area - garden area = path area (given as 192 sq/ft)<BR>\n" );
document.write( "(4x^2 + 52x + 165) - 165 = 192<BR>\n" );
document.write( "4x^2 + 52x + 165 - 165 - 192 = 0<BR>\n" );
document.write( "4x^2 + 52x - 192 = 0<BR>\n" );
document.write( "Simplify, divide by 4<BR>\n" );
document.write( "x^2 + 13x - 48<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x + 16)(x - 3) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "x = 3 ft is the width of the garden path<BR>\n" );
document.write( "Check<BR>\n" );
document.write( "(21*17) - (15*11) = <BR>\n" );
document.write( "357 - 165 = 192<BR>\n" );
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document.write( "2.A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?<BR>\n" );
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document.write( "Let r = interest in decimal form<BR>\n" );
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document.write( "(x+1)(8000(x+1) + 2500) = 11445<BR>\n" );
document.write( "(x+1)(8000x + 8000 + 2500) = 11445<BR>\n" );
document.write( "(x+1)(8000x + 10500) = 11445<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "8000x^2 + 18500x + 10500 = 11445<BR>\n" );
document.write( "8000x^2 + 18500x + 10500 - 11445 = 0<BR>\n" );
document.write( "8000x^2 + 18500x - 945<BR>\n" );
document.write( "Simplify divide by 5<BR>\n" );
document.write( "1600x^2 + 3700x - 189 = 0<BR>\n" );
document.write( "Solve this using the quadratic formula,<BR>\n" );
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document.write( "3.Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.<BR>\n" );
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document.write( "Let s = \"that certain speed\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+20) = the faster speed<BR>\n" );
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document.write( "Write a time equation: time = dist/speed<BR>\n" );
document.write( "Actual time = faster speed time + 2 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fs ALIGN=MIDDLE  ALT=\"150%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28%28s%2B20%29%29 ALIGN=MIDDLE  ALT=\"150%2F%28%28s%2B20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( "Solve this equation for s<BR>\n" );
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document.write( "4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water? <BR>\n" );
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document.write( "Let s = speed in still water<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = speed down stream<BR>\n" );
document.write( "(s-5) = speed up stream<BR>\n" );
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document.write( "time downstream + time upstream = 6 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"40%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"40%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
document.write( "Solve for s </SPAN>\n" );
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