document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117445>Question 1117445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Mr. Gardener has two kinds of solutions containing fertilizer and water. One of the solutions is 10% fertilizer and the other is 30% fertilizer. Mr. Gardener needs 200 liters of a 24% fertilizer solution. How much of the 10% solution should Mr. Gardener use in order to have the 24% fertilizer solution?\r<BR>\n" );
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document.write( "2. The top floor of the school building is a rectangle whose perimeter is 320 feet. The width is 30 feet less than the length. What is the width of the rectangle?\r<BR>\n" );
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document.write( "3. Jane can clean the living room in 3 hours, Kai in 6 hours, and Dana in 8 hours. If they work together, in how many minutes can they clean the entire room?\r<BR>\n" );
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document.write( "4. Rachelle invested part of $185 000 at 7% and the rest 9%. If the interest from 9% investment is $1 450 more than the interest earned at the 7% investment. How much did she invest at the 9% rate?\r<BR>\n" );
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document.write( "5. Joy's house, the supermarket, and Marty's office are on a straight road. Joy rode her car and traveled with a speed of 60 kph for 10 minutes. Marty left his office to meet Joy at the supermarket. He used his car and traveled at the speed of 90 kph for 5 mins. How far is Marty's office from Joy's house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732529 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Mr. Gardener has two kinds of solutions containing fertilizer and water. One of the solutions is 10% fertilizer and the other is 30% fertilizer. Mr. Gardener needs 200 liters of a 24% fertilizer solution. How much of the 10% solution should Mr. Gardener use in order to have the 24% fertilizer solution? \r<BR>\n" );
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document.write( "x = 10% solution<BR>\n" );
document.write( "y = 30% solution<BR>\n" );
document.write( "x + y = 200<BR>\n" );
document.write( ".1x + .3y = .24 * (x + y) = .24 * 200 = 48<BR>\n" );
document.write( "equations become:<BR>\n" );
document.write( "x + y = 200<BR>\n" );
document.write( ".1x + .3y = 48<BR>\n" );
document.write( "solve for x from first equation to get x = 200 - y<BR>\n" );
document.write( "replace x with 200 - y in second equation to get:<BR>\n" );
document.write( ".1(200 - y) + .3y = 48<BR>\n" );
document.write( "simplify to get 20 - .1y + .3y = 48<BR>\n" );
document.write( "combine like terms to get 20 + .2y = 48<BR>\n" );
document.write( "solve for y to get y = (48 - 20) / .2 = 140<BR>\n" );
document.write( "that makes x = 60<BR>\n" );
document.write( "you have x = 60 and y = 140<BR>\n" );
document.write( "60 + 140 = 200<BR>\n" );
document.write( ".1 * 60 + .3 * 140 = 48<BR>\n" );
document.write( "48 / 200 = .24<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "you need 60 liters of the 10% solution mixed with 140 liters of the 30% solution.\r<BR>\n" );
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document.write( "2. The top floor of the school building is a rectangle whose perimeter is 320 feet. The width is 30 feet less than the length. What is the width of the rectangle? \r<BR>\n" );
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document.write( "perimeter= 2L +2W, therefore 2L + 2W = 320<BR>\n" );
document.write( "W = L - 30<BR>\n" );
document.write( "replace W with L - 30 to get:<BR>\n" );
document.write( "2L + 2(L - 30) = 320<BR>\n" );
document.write( "simplify to get 4L - 60 = 320<BR>\n" );
document.write( "add 60 to both sides of the equaiton to get 4L = 380<BR>\n" );
document.write( "solve for L to get L = 95<BR>\n" );
document.write( "W = L - 30 makes W = 65<BR>\n" );
document.write( "2L = 2 * 95 = 190<BR>\n" );
document.write( "2W = 2 * 65 = 130<BR>\n" );
document.write( "2L + 2W = 320<BR>\n" );
document.write( "solution is that the width of the rectangle is 65 feet.\r<BR>\n" );
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document.write( "3. Jane can clean the living room in 3 hours, Kai in 6 hours, and Dana in 8 hours. If they work together, in how many minutes can they clean the entire room?\r<BR>\n" );
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document.write( "rate * time = quantity<BR>\n" );
document.write( "quantity = 1 living room.<BR>\n" );
document.write( "time = hours.<BR>\n" );
document.write( "rate = fraction of the job done in 1 hour.<BR>\n" );
document.write( "jane takes 3 hours.<BR>\n" );
document.write( "her rate is therefore 1/3 of the job in 1 hour.<BR>\n" );
document.write( "kai takes 6 hours<BR>\n" );
document.write( "here rate is therefore 1/6 of the job in 1 hour.<BR>\n" );
document.write( "dana takes 8 hours.<BR>\n" );
document.write( "her rate is therefore 1/8 of the job in 1 hour.<BR>\n" );
document.write( "when they work together, their rates are added together.<BR>\n" );
document.write( "you get (1/3 + 1/6 + 1/8) * time = 1<BR>\n" );
document.write( "least common multiple is 24.<BR>\n" );
document.write( "formula becomes (8/24 + 4/24 + 3/24) * time = 1<BR>\n" );
document.write( "combine like terms to get 15/24 * time = 1<BR>\n" );
document.write( "solve for time to get time = 24/15 hours.<BR>\n" );
document.write( "there are 60 minutes in an hour, therefore 24/15 * 60 = 96 minutes<BR>\n" );
document.write( "working together, it will take them 96 minutes to clean the living room.\r<BR>\n" );
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document.write( "4. Rachelle invested part of $185000 at 7% and the rest at 9%. If the interest from 9% investment is $1450 more than the interest earned at the 7% investment. How much did she invest at the 9% rate?\r<BR>\n" );
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document.write( "x = amount invested at 7%<BR>\n" );
document.write( "y = amount imvested at 9%<BR>\n" );
document.write( "x + y = 185000<BR>\n" );
document.write( "interest earned from 9% investment is 1450 more than interest earned from 7% investment.<BR>\n" );
document.write( "this means .09y = .07x + 1450<BR>\n" );
document.write( "solve for y to get y = (.07x + 1450)/.09<BR>\n" );
document.write( "in x + y = 185000, replace y with (.07x + 1450) / .09 to get:<BR>\n" );
document.write( "x + (.07x + 1450)/.09 = 185000<BR>\n" );
document.write( "multiply both sides of this equation by .09 to get:<BR>\n" );
document.write( ".09x + .07x + 1450 = 16650<BR>\n" );
document.write( "combine like terms and subtract 1450 from both sides to get:<BR>\n" );
document.write( ".16x = 15200.<BR>\n" );
document.write( "solve for x to get x = 15200 / .16 = 95000<BR>\n" );
document.write( "that makes y = 185000 - 95000 = 90000<BR>\n" );
document.write( "x + y becomes 95000 + 90000 = 185000<BR>\n" );
document.write( "interest earned on 7% investment = .07 * 95000 = 6650<BR>\n" );
document.write( "interest earned on 9% investment = .09 * 90000 = 8100<BR>\n" );
document.write( "8100 - 6650 = 1450<BR>\n" );
document.write( "interested earned on 9% investment is 1450 more than interest earned on 9% investment.<BR>\n" );
document.write( "everything looks good.<BR>\n" );
document.write( "your solution is that she invested 90000 at 9% rate of return.\r<BR>\n" );
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document.write( "5. Joy's house, the supermarket, and Marty's office are on a straight road. Joy rode her car and traveled with a speed of 60 kph for 10 minutes. Marty left his office to meet Joy at the supermarket. He used his car and traveled at the speed of 90 kph for 5 mins. How far is Marty's office from Joy's house?\r<BR>\n" );
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document.write( "rate * time = distance<BR>\n" );
document.write( "minutes / 60 = hours<BR>\n" );
document.write( "joy traveled 60 kph * 10/60 hours = 10 kilometers.<BR>\n" );
document.write( "marty traveled 90 * 5/60 = 7.5 kilometers.<BR>\n" );
document.write( "they met at the supermarket.<BR>\n" );
document.write( "marty's office is 10 + 7.5 = 17.5 kilometers from joy's house.\r<BR>\n" );
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document.write( "any questions, send email to dtheohilis@gmail.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
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