document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157116>Question 1157116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The sum of two numbers is 30. Five times the smaller exceeds twice the larger by 17. Find the numbers.<BR>\n" );
document.write( "2. Tim is 1/5 as old as Tom. In six years, Tim will be 1/3 as old. Find their present ages.<BR>\n" );
document.write( "3. A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the two investments is $1456, how much does he have invested at each rate?<BR>\n" );
document.write( "4. How many gallons of cottonseed oil must be added to 45 gallons of a solution of olive oil, which is 90% olive oil, in order to make the resulting solution 80% olive oil?<BR>\n" );
document.write( "5. Tea worth $4.10 per pound is to be mixed with tea worth $4.90 per pound. How many pounds of each should be used to obtain 25 lb. of a blend worth $4.40 per pound?\r<BR>\n" );
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document.write( "i hope you can help me for this... although my teacher gave me a sample but i can't understand... thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779922 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>1. The sum of two numbers is 30. Five times the smaller exceeds twice the larger by 17. Find the numbers.</i><BR>\n" );
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document.write( "Smaller number = x<BR>\n" );
document.write( "Larger number = 30 - x<BR>\n" );
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document.write( "5x = 2(30 - x) + 17<BR>\n" );
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document.write( "5x = 60 - 2x + 17<BR>\n" );
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document.write( "5x = 77 - 2x<BR>\n" );
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document.write( "7x = 77<BR>\n" );
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document.write( "x = 11<BR>\n" );
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document.write( "Smaller number = x = <b>11</b><BR>\n" );
document.write( "Larger number = 30 - x = 30 - 11 = <b>19</b><BR>\n" );
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document.write( "<i>2. Tim is 1/5 as old as Tom. In six years, Tim will be 1/3 as old. Find their present ages.</i><BR>\n" );
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document.write( "Tom's age = x<BR>\n" );
document.write( "Tim's age = x/5<BR>\n" );
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document.write( "(x + 6)/3 = x/5 + 6<BR>\n" );
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document.write( "x/3 + 2 = x/5 + 6<BR>\n" );
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document.write( "x/3 - x/5 = 4<BR>\n" );
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document.write( "5x/15 - 3x/15 = 4<BR>\n" );
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document.write( "2x/15 = 4<BR>\n" );
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document.write( "2x = 60<BR>\n" );
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document.write( "x = 30<BR>\n" );
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document.write( "Tom's age = x = <b>30</b><BR>\n" );
document.write( "Tim's age = x/5 = 30/5 = <b>6</b><BR>\n" );
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document.write( "<i>3. A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the two investments is $1456, how much does he have invested at each rate?</i><BR>\n" );
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document.write( "<u>12% rate</u><BR>\n" );
document.write( "Principal = p<BR>\n" );
document.write( "Rate = 0.12<BR>\n" );
document.write( "Interest = 0.12p<BR>\n" );
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document.write( "<u>8% rate</u><BR>\n" );
document.write( "Principal = 15000 - p<BR>\n" );
document.write( "Rate = 0.08<BR>\n" );
document.write( "Interest = 0.08(15000 - p) = 1200 - 0.08p<BR>\n" );
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document.write( "0.12p + (1200 - 0.08p) = 1456<BR>\n" );
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document.write( "0.12p + 1200 - 0.08p = 1456<BR>\n" );
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document.write( "0.04p = 256<BR>\n" );
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document.write( "p = 6400<BR>\n" );
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document.write( "<u>12% rate</u><BR>\n" );
document.write( "Principal = p = <b>$6400</b><BR>\n" );
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document.write( "<u>8% rate</u><BR>\n" );
document.write( "Principal = 15000 - p = 15000 - 6400 = <b>$8600</b><BR>\n" );
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document.write( "<i>4. How many gallons of cottonseed oil must be added to 45 gallons of a solution of olive oil, which is 90% olive oil, in order to make the resulting solution 80% olive oil?</i><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.90%2845%29%2F%2845+%2B+x%29 ALIGN=MIDDLE  ALT=\"0.90%2845%29%2F%2845+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.80<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40.5%2F%2845+%2B+x%29 ALIGN=MIDDLE  ALT=\"40.5%2F%2845+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.80<BR>\n" );
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document.write( "0.80(45 + x) = 40.5<BR>\n" );
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document.write( "36 + 0.80x = 40.5<BR>\n" );
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document.write( "0.80x = 4.5<BR>\n" );
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document.write( "x = <b>5.625</b><BR>\n" );
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document.write( "<i>5. Tea worth $4.10 per pound is to be mixed with tea worth $4.90 per pound. How many pounds of each should be used to obtain 25 lb. of a blend worth $4.40 per pound?</i><BR>\n" );
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document.write( "Pounds of $4.10 tea = x<BR>\n" );
document.write( "Pounds of $4.90 tea = y<BR>\n" );
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document.write( "x + y = 25<BR>\n" );
document.write( "4.10x + 4.90y = 25(4.40)<BR>\n" );
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document.write( "x + y = 25<BR>\n" );
document.write( "4.10x + 4.90y = 110<BR>\n" );
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document.write( "Multiply first equation by -4.90:<BR>\n" );
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document.write( "-4.90x - 4.90y = -122.50<BR>\n" );
document.write( "4.10x + 4.90y = 110<BR>\n" );
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document.write( "Add both equations together:<BR>\n" );
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document.write( "-0.80x = -12.50<BR>\n" );
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document.write( "x = 15.625<BR>\n" );
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document.write( "We now know x = 15.625.  To find y, we simply plug that into:<BR>\n" );
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document.write( "x + y = 25<BR>\n" );
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document.write( "15.625 + y = 25<BR>\n" );
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document.write( "y = 9.375<BR>\n" );
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document.write( "Pounds of $4.10 tea = x = <b>15.625</b><BR>\n" );
document.write( "Pounds of $4.90 tea = y = <b>9.375</b> </SPAN>\n" );
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