document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143667>Question 143667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a lot of trouble with word problem questions.  If someone could help me that would be great.  If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!\r<BR>\n" );
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document.write( "*In a certain medical test designed to measure carbohydrate tolerance, and adult drinks 7 ounces of a 30% glucose solution.  When the test is administered to a child, the glucose concentration must be decreased to 20%.  How much 30% glucose solution and how much water should be used to prepare 7 ounces of 20% glucose solution?\r<BR>\n" );
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document.write( "*Theophylline, is prepared from an elixir with a drug concentration of 5 mg/ml and a cherry-flavored syrup that is to be added to hide the taste of the drug.  How much of each must be used tp prepare 100 mililiters of solution with a drug concentratio of 2 mg/ml?\r<BR>\n" );
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document.write( "*Two children who are 224 meters apart, start walking toward each other at the same instant at rates of 1.5m/sec and 2 m/sec, respectively.<BR>\n" );
document.write( "(a) When will they meet?<BR>\n" );
document.write( "(b) How far will each have walked?\r<BR>\n" );
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document.write( "*A wafer cone is to hold 8 in^3 of ice cream when filled to the bottom.  The diameter of the cone is 2 inches, and the top of the ice cream has the shape of a hemisphere.  Find the height (h) of the cone.\r<BR>\n" );
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document.write( "*A runner starts at the beginning of a runners' path and runs at a constant rate of 6 mi/hr.  Five minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course.  How long will it take the second runner to reach the first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104554 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=104554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a certain medical test designed to measure carbohydrate tolerance, and adult drinks 7 ounces of a 30% glucose solution. When the test is administered to a child, the glucose concentration must be decreased to 20%. How much 30% glucose solution and how much water should be used to prepare 7 ounces of 20% glucose solution?<BR>\n" );
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document.write( "Let x = amt of 30% glucose solution<BR>\n" );
document.write( "We want the resulting total to be 7 oz, therefore<BR>\n" );
document.write( "(7-x) = amt of water required (water is a 0% solution)<BR>\n" );
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document.write( "A percent glucose equation.<BR>\n" );
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document.write( "The amt of glucose remains the same, (the percent changes by adding water)<BR>\n" );
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document.write( ".30x = .20(7)<BR>\n" );
document.write( ".3x = 1.4<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4%2F.3 ALIGN=MIDDLE  ALT=\"1.4%2F.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 4<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;\" > oz of 30% solution<BR>\n" );
document.write( "then<BR>\n" );
document.write( "7 - 4<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;\" > = 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > oz of water<BR>\n" );
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document.write( "*Theophylline, is prepared from an elixir with a drug concentration of 5 mg/ml and a cherry-flavored syrup that is to be added to hide the taste of the drug. How much of each must be used to prepare 100 milliliters of solution with a drug concentration of 2 mg/ml?<BR>\n" );
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document.write( "Let x = amt of 5 mg elixir required<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(100-x) = amt of syrup required<BR>\n" );
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document.write( "5x = 2(100)<BR>\n" );
document.write( "5x = 200<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F5 ALIGN=MIDDLE  ALT=\"200%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 40 ml of elixir<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100-40 = 60 ml of syrup <BR>\n" );
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document.write( "*Two children who are 224 meters apart, start walking toward each other at the same instant at rates of 1.5m/sec and 2 m/sec, respectively.<BR>\n" );
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document.write( "The total distance of both will equal 224 meters. Write a distance equation:<BR>\n" );
document.write( "Dist = speed * time<BR>\n" );
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document.write( "(a) When will they meet?<BR>\n" );
document.write( "Let t = time (in sec) when they meet:<BR>\n" );
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document.write( "child 1 dist + child 2 dist = 224 meters<BR>\n" );
document.write( "1.5t + 2t = 224<BR>\n" );
document.write( "3.5t = 224<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224%2F3.5 ALIGN=MIDDLE  ALT=\"224%2F3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 64 seconds<BR>\n" );
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document.write( "(b) How far will each have walked?<BR>\n" );
document.write( "now we know t<BR>\n" );
document.write( "1.5*64 = 96 meters (child 1)<BR>\n" );
document.write( "2.0*64 = 128 meters (child 2)<BR>\n" );
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document.write( "total = 224, confirms our solution<BR>\n" );
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document.write( "*A wafer cone is to hold 8 in^3 of ice cream when filled to the bottom. The diameter of the cone is 2 inches, and the top of the ice cream has the shape of a hemisphere. Find the height (h) of the cone.<BR>\n" );
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document.write( "The vol of a cone + the vol of half sphere = 8 cu in<BR>\n" );
document.write( "r=1 in (half the diameter<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<BR>\n" );
document.write( "using the given values for r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2A1%5E2%2Ah ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2A1%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Api%2A1%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Api%2A1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2A1%2Ah ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2A1%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Api%2A1 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Api%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<BR>\n" );
document.write( "Use a calc<BR>\n" );
document.write( "1.0472h + 1.5708 = 8<BR>\n" );
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document.write( "1.0472h = 8 - 1.5708<BR>\n" );
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document.write( "1.0472h = 6.4292<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.4292%2F1.0472 ALIGN=MIDDLE  ALT=\"6.4292%2F1.0472\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 6.14 inches the height of the cone part only, the part including hemisphere would be an inch higher, 7.14\"<BR>\n" );
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document.write( "*A runner starts at the beginning of a runners' path and runs at a constant rate of 6 mi/hr. Five minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. How long will it take the second runner to reach the first?<BR>\n" );
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document.write( "We know that when the 2nd runner catches up with the 1st, they will have run the same distance.<BR>\n" );
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document.write( "Change 5 min to hrs: 5/60 = 1/12<BR>\n" );
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document.write( "Let t = run time of the 2nd runner<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = run time of the 1st runner<BR>\n" );
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document.write( "Write a dist equation: Dist = speed * time<BR>\n" );
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document.write( "Fast runner dist = slow runner dist<BR>\n" );
document.write( "8t = 6(t+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "8t = 6t + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8t - 6t - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr or we can say 15 min for the 2nd runner to catch the 1st<BR>\n" );
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document.write( "We can check solution by finding the distance traveled by each runner (should be equal)<BR>\n" );
document.write( "1st runners time = 20 min, 2nd runner 15 min<BR>\n" );
document.write( "6 * (20/60) = 2 mi<BR>\n" );
document.write( "8 * (15/60) = 2 mi<BR>\n" );
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document.write( "Hope you can follow all this, you can ask me about it until 9:15 central daylight or tomorrow. ankor@dixie-net.com\r<BR>\n" );
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