document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54277>Question 54277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help solving these four questions:\r<BR>\n" );
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document.write( "1.  How many pounds of coffee beans selling for $2.80 per pound should be mixed with 2 pounds of coffee beans selling for $1.60 a pound to obtain mixture selling for $2.56 per pound?\r<BR>\n" );
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document.write( "2.  Two trains, an express and a commuter, are 450 miles apart.  Both start at the same time and travel toward each other.  The meet 6 hours later.  The speed of the express is 25 mph faster that the commuter.  Find the speed of each train.\r<BR>\n" );
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document.write( "3.  Two cars are traveling in opposite directions at average rates of 60 mph and 72 mph.  How many hours will it take before the ars are 198 miles apart?\r<BR>\n" );
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document.write( "4.  One thousand two hundred people attended a college basketball game.  Student tickets cost $4 and all other tickets cost $15.  If the receipts for the game totaled $12,786, how many of each kind of ticket was sold?\r<BR>\n" );
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document.write( "5.  A train traveling at 40 miles per hour leaves for a certain town.  One hour later, a bus traveling at 50miles per hour leaves for the same town and arrives at the same time as the train.  If both the train and the bus traveled in a straight line, how far is the town from where they started?\r<BR>\n" );
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document.write( "6.  A landscaper has a budget of $2250 to palnt 100 azaeleas and rhododendrons around a new office building.  If there is a cost of $40 per rhododendron and $15 per azalea, how many of each can she plant?\r<BR>\n" );
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document.write( "When you give the answers please identify the variable, write the equation and show me how to solve the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36588 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am going to show you step by step solutions for 2 and give you hints on the other 4.  If you have more questions, let me know.<BR>\n" );
document.write( "1.<BR>\n" );
document.write( "If the amount of $2.80 coffee =x<BR>\n" );
document.write( "And the amount of $1.60 coffe =2 lbs<BR>\n" );
document.write( "Then the amoung you have when you mix them together is: x+2<BR>\n" );
document.write( "The price of $2.80 = 280 cents (it's easier to solve without decimals)<BR>\n" );
document.write( "The price of $1.60 = 160<BR>\n" );
document.write( "The price of the mixture $2.56=256 <BR>\n" );
document.write( "Cost = Price*amount, so our equation is:<BR>\n" );
document.write( "280x+160(2)=256(x+2)<BR>\n" );
document.write( "280x+320=256x+512<BR>\n" );
document.write( "-256x+280x+320=-256x+256x+512<BR>\n" );
document.write( "24x+320=512<BR>\n" );
document.write( "24x+320-320=512-320<BR>\n" );
document.write( "24x=192<BR>\n" );
document.write( "24x/24=192/24<BR>\n" );
document.write( "x=8 <BR>\n" );
document.write( "The amount of $2.80 coffe that should be added is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288+lbs%29 ALIGN=MIDDLE  ALT=\"highlight%288+lbs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check by substituting 8 in for x<BR>\n" );
document.write( "$2.80(8)+$1.60(2)=$2.56(8+2)<BR>\n" );
document.write( "$22.40+$3.20=$2.56(10)<BR>\n" );
document.write( "$25.60=$25.60  Seems reasonable.<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "The trains are 450 miles apart and heading toward each other, so if we add their distances together we will get a total of 450 miles.<BR>\n" );
document.write( "The formula you need to learn is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=rt%29 ALIGN=MIDDLE  ALT=\"highlight%28d=rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where d= distance, r=rate or speed, and t=time.<BR>\n" );
document.write( "They both travel a time of 6 hrs, so<BR>\n" );
document.write( "Let time for the commuter train=6<BR>\n" );
document.write( "Let time for the express train=6<BR>\n" );
document.write( "Let RATE for the commuter train=x  (because we don't know anything about it)<BR>\n" );
document.write( "Then RATE for the express train=x+25  (because it's 25 mph faster than the commuter train)<BR>\n" );
document.write( "Then the distance for the commuter train is: 6x<BR>\n" );
document.write( "The distance for the express is: 6(x+25)<BR>\n" );
document.write( "The total distance:450 <BR>\n" );
document.write( "PROBLEM to solve:<BR>\n" );
document.write( "6x+6(x+25)=450<BR>\n" );
document.write( "6x+6x+150=450<BR>\n" );
document.write( "(6+6)x+150=450<BR>\n" );
document.write( "12x+150=450<BR>\n" );
document.write( "12x+150-150=450-150<BR>\n" );
document.write( "12x=300<BR>\n" );
document.write( "12x/12=300/12<BR>\n" );
document.write( "x=25<BR>\n" );
document.write( "The rate of the commuter train: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=25+mph%29 ALIGN=MIDDLE  ALT=\"highlight%28x=25+mph%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rate of the express train: x+25=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2825%2B25=50+mph%29 ALIGN=MIDDLE  ALT=\"highlight%2825%2B25=50+mph%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "6(25)+6(50)=450<BR>\n" );
document.write( "150+300=450<BR>\n" );
document.write( "450=450 Seems reasonalbe.<BR>\n" );
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document.write( "3.  Add the two distances together to get 198 (because they're travelling in opposite directions to add up to 198 miles apart.)<BR>\n" );
document.write( "  Let the time for both =t (because they're both traveling the same amount of time)<BR>\n" );
document.write( "Formula to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=rt%29 ALIGN=MIDDLE  ALT=\"highlight%28d=rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "4.  Let the amount of students =x<BR>\n" );
document.write( "Then all of the rest of the tickets= 1200-x<BR>\n" );
document.write( "Then your problem is:<BR>\n" );
document.write( "4x+15(1200-x)=12,786<BR>\n" );
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document.write( "5. Let the time that the train traveled = t<BR>\n" );
document.write( "Then the time that the bus traveled=t-1 (one hour less)<BR>\n" );
document.write( "Set the two distances = to each other because they are traveling to the same town in a straight line.<BR>\n" );
document.write( "Fromula to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=rt%29 ALIGN=MIDDLE  ALT=\"highlight%28d=rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "6. Let the amount of rhododendrons=x<BR>\n" );
document.write( "Then the amount of azaleas would = the rest of the 100 plants: 100-x<BR>\n" );
document.write( "Set the problem up like #4.<BR>\n" );
document.write( "Happy Calculating!!!<BR>\n" );
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