document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69076>Question 69076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If someone could help me out with these I'll appreciated. THank you.\r<BR>\n" );
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document.write( "Problem#6\r<BR>\n" );
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document.write( "Directions: Solve the following word problems.\r<BR>\n" );
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document.write( "Number problem. If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?\r<BR>\n" );
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document.write( "Problem# 18 same directions<BR>\n" );
document.write( "Science and medicine. A passenger train can travel 325 mi in the same time a<BR>\n" );
document.write( "freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, find the speed of each.\r<BR>\n" );
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document.write( "Problem#22 same directions<BR>\n" );
document.write( "Science and medicine. Ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?\r<BR>\n" );
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document.write( "Problem#26 same directions<BR>\n" );
document.write( "Science and medicine. A plane flies 720 mi against a steady 30-mi/h headwind<BR>\n" );
document.write( "and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane’s speed in still air?\r<BR>\n" );
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document.write( "Problem# 34. same directions\r<BR>\n" );
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document.write( "Business and finance. Kevin earned $165 interest for 1 year on an investment of<BR>\n" );
document.write( "$1500. At the same rate, what amount of interest would be earned by an investment<BR>\n" );
document.write( "of $2500?\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 #49229 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=49229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem#6<BR>\n" );
document.write( "Directions: Solve the following word problems.<BR>\n" );
document.write( "Number problem. If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?<BR>\n" );
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document.write( "Let x = one integer;  and (x+1) = next consecutive integer<BR>\n" );
document.write( "A lot less typing if we use decimals. (3/5) = .6<BR>\n" );
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document.write( ".6(x+1) - .5x = 3<BR>\n" );
document.write( ".6x + .6 - .5x = 3<BR>\n" );
document.write( ".1x = 3 - .6<BR>\n" );
document.write( ".1x = 2.4<BR>\n" );
document.write( "x = 2.4/.1<BR>\n" );
document.write( "x = 24 and 25 are the integers:<BR>\n" );
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document.write( "Check: <BR>\n" );
document.write( ".6(25) - .5(24) = <BR>\n" );
document.write( "  15 - 12 = 3<BR>\n" );
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document.write( "Problem# 18 same directions<BR>\n" );
document.write( "Science and medicine. A passenger train can travel 325 mi in the same time a<BR>\n" );
document.write( "freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, find the speed of each.<BR>\n" );
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document.write( "Let s = speed of the freight<BR>\n" );
document.write( "Then (s+25) = Pass train<BR>\n" );
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document.write( "Time = dist/speed<BR>\n" );
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document.write( "Freight time = Pass time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=325%2F%28%28s%2B25%29%29 ALIGN=MIDDLE  ALT=\"325%2F%28%28s%2B25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cross multiply:<BR>\n" );
document.write( "325s = 200(s+25)<BR>\n" );
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document.write( "325s = 200s + 5000<BR>\n" );
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document.write( "325s - 200s = 5000<BR>\n" );
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document.write( "125s = 5000<BR>\n" );
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document.write( "s = 5000/125<BR>\n" );
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document.write( "s = 40 mph is the speed of the freight<BR>\n" );
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document.write( "40 + 25 = 65 mph is the speed of the pass train<BR>\n" );
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document.write( "Check to see if, in fact, the times are equal: <BR>\n" );
document.write( "325/65 = 200/40<BR>\n" );
document.write( "  5  =  5<BR>\n" );
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document.write( "Problem#22 same directions<BR>\n" );
document.write( "Science and medicine. Ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?<BR>\n" );
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document.write( "Let t = her time on the 1st day<BR>\n" );
document.write( "Then (t-2) = her time on the 2nd day<BR>\n" );
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document.write( "Speed = Dist/time<BR>\n" );
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document.write( "1st day speed = 2nd day speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Ft ALIGN=MIDDLE  ALT=\"360%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2F%28%28t-2%29%29 ALIGN=MIDDLE  ALT=\"270%2F%28%28t-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cross multiply and you have:<BR>\n" );
document.write( "360(t-2) = 270t<BR>\n" );
document.write( "360t - 720 = 270t<BR>\n" );
document.write( "360t - 270t = +720<BR>\n" );
document.write( "90t = 720<BR>\n" );
document.write( "t = 720/90<BR>\n" );
document.write( "t = 8 hrs the 1st day<BR>\n" );
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document.write( "8 - 2 = 6 hrs the 2nd day<BR>\n" );
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document.write( "Check to see if the speeds are equal:<BR>\n" );
document.write( "360/8 = 270/6<BR>\n" );
document.write( " 45 = 45<BR>\n" );
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document.write( "Problem#26 same directions<BR>\n" );
document.write( "Science and medicine. A plane flies 720 mi against a steady 30-mi/h headwind<BR>\n" );
document.write( "and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane’s speed in still air?<BR>\n" );
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document.write( "Let s = speed in still air:<BR>\n" );
document.write( "Then:<BR>\n" );
document.write( "(s-30) = speed against the wind<BR>\n" );
document.write( "(s+30) = speed with the wind<BR>\n" );
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document.write( "Time = dist/speed<BR>\n" );
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document.write( "Against time + with time = 10 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28%28s-3%29%29 ALIGN=MIDDLE  ALT=\"720%2F%28%28s-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28%28s%2B30%29%29 ALIGN=MIDDLE  ALT=\"720%2F%28%28s%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10<BR>\n" );
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document.write( "Multiply equation by (s-30)(s+30) to get rid of the denominators:<BR>\n" );
document.write( "720(s+30) + 720(s-30) = 10(s-30)(s+30)<BR>\n" );
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document.write( "720s + 21600 + 720s - 21600 = 10(s^2 - 900)<BR>\n" );
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document.write( "720s + 21600 + 720s - 21600 = 10s^2 - 9000; (21600 is eliminated)<BR>\n" );
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document.write( "1440s = 10s^2 - 9000<BR>\n" );
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document.write( "10s^2 - 1440s - 9000 = 0; our old friend the quadratic equation<BR>\n" );
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document.write( "Simplify, divide by 10<BR>\n" );
document.write( "s^2 - 144x - 900 = 0<BR>\n" );
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document.write( "Factor to:<BR>\n" );
document.write( "(s-150)(s+6) = 0<BR>\n" );
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document.write( "S = +150 mph speed in still air, (s=-6 is ignored, obviously)<BR>\n" );
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document.write( "Check using the time:<BR>\n" );
document.write( "720/120) + 720/180 =<BR>\n" );
document.write( " 6 + 4 = 10<BR>\n" );
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document.write( "Problem# 34. same directions<BR>\n" );
document.write( "Business and finance. Kevin earned $165 interest for 1 year on an investment of<BR>\n" );
document.write( "$1500.<BR>\n" );
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document.write( "Remember P*R*T = I; substitute for P and T and I, find R<BR>\n" );
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document.write( "1500 * R * 1 = 165<BR>\n" );
document.write( "1500R = 165<BR>\n" );
document.write( "R = 165/1500<BR>\n" );
document.write( "R = .11 or 11%<BR>\n" );
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document.write( "Check using the I = PRT formula<BR>\n" );
document.write( "I = 1500*.11*1<BR>\n" );
document.write( "I = $165<BR>\n" );
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document.write( "At the same rate, what amount of interest would be earned by an investment of $2500?<BR>\n" );
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document.write( "I = 2500*.11*1<BR>\n" );
document.write( "I = $275 amt of interest earned on $2500 at a rate of 11%<BR>\n" );
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document.write( "A lot of steps here I hope you will satisfy yourself that you understand each. <BR>\n" );
document.write( "If you have a question on any of these procedures, you can email me.  <BR>\n" );
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