document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100495>Question 1100495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "a tank with a square base of sides 10cm was 3/4 filled with water. Half the amount of water was poured into an empty container filling it to the brim.two thirds of the amount of water in the container<BR>\n" );
document.write( "was poured into a basin which was already one fifth filled with 700cm^3 of water. The basin was then half full.\r<BR>\n" );
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document.write( "what was the original water level in the tank<BR>\n" );
document.write( "what was the height of the tank. \r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715128 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=715128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let T be the amount of water that the tank can hold.<BR>\n" );
document.write( "let C be the amount of water that the container can hold.<BR>\n" );
document.write( "let B be the amount of water that the basin can hold.\r<BR>\n" );
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document.write( "the tank is 3/4 filled with water, therefore you start with 3/4 * T.\r<BR>\n" );
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document.write( "you pour half the amount of water that's in the tank into a container and the container is filled to the brim.\r<BR>\n" );
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document.write( "therefore C = 1/2 * 3/4 * T which becomes:\r<BR>\n" );
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document.write( "C = 3/8 * T\r<BR>\n" );
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document.write( "you pour 2/3 of the water that's in the container into the basin which already has 700 cm^3 of water in it and the basin becomes half full.\r<BR>\n" );
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document.write( "therefore 2/3 * C + 700 = 1/2 * B\r<BR>\n" );
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document.write( "you are told that 700 cm^3 of water equals 1/5 the amount of water that the basin can hold.\r<BR>\n" );
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document.write( "therefore, the amount of water that the basin can hold is 5 * 700 = 3500 cm^3 of water.\r<BR>\n" );
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document.write( "therefore B = 3500\r<BR>\n" );
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document.write( "from the equation of 2/3 * C + 700 = 1/2 * B, replace B with 3500 to get:\r<BR>\n" );
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document.write( "2/3 * C + 700 = 1/2 * (3500) which becomes:\r<BR>\n" );
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document.write( "2/3 * C + 700 = 1750\r<BR>\n" );
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document.write( "solve for C to get:\r<BR>\n" );
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document.write( "C = (1750 - 700) / (2/3) = 1575\r<BR>\n" );
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document.write( "from the equation of C = 3/8 * T, replace C with 1575 to get:\r<BR>\n" );
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document.write( "1575 = 3/8 * T\r<BR>\n" );
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document.write( "solve for T to get:\r<BR>\n" );
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document.write( "T = 1575 / (3/8) which becomes:\r<BR>\n" );
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document.write( "T = 4200\r<BR>\n" );
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document.write( "the original amount of water that was in the tank was 3/4 * 4200 = 3150 cm^3.\r<BR>\n" );
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document.write( "the volume of water in the tank is given by the formula:\r<BR>\n" );
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document.write( "V = area of the base * the height.\r<BR>\n" );
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document.write( "the area of the base is 10 * 10 = 100 cm^2.\r<BR>\n" );
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document.write( "the formula becomes 4200 = 100 * the height.\r<BR>\n" );
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document.write( "the height of the tank is therefore equal to 4200 / 100 = 42 cm.\r<BR>\n" );
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document.write( "the height of the original water level in the tank would be 3/4 * 42 = 31.5 cm.\r<BR>\n" );
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document.write( "to confirm if the solution is correct, do the following.\r<BR>\n" );
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document.write( "the tank is 3/4 full, therefore the amount of water in the tank is 3/4 * 4200 = 3150 cm^3.\r<BR>\n" );
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document.write( "you fill the container with half of this, therefore the amount of water in the container is 1/2 * 3150 = 1575 cm^3.\r<BR>\n" );
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document.write( "you take 2/3 of this and add it to 700 cm^3 of water already in the basin and you get 2/3 * 1575 + 300 = 1750 cm^3 of water in the basin.\r<BR>\n" );
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document.write( "this amount of water makes the basin half full, therefore a full basin of water can hold 2 * 1750 = 3500 cm^3 of water.\r<BR>\n" );
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document.write( "1/5 of this is 3500 / 5 = 700 cm^3 of water which is what you were given.\r<BR>\n" );
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document.write( "everything checks out so the solution looks good.\r<BR>\n" );
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document.write( "the height of the original amount of water in the tank was 31.5 cm.\r<BR>\n" );
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document.write( "the height of the full tank was 42 cm.\r<BR>\n" );
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document.write( "the original amount of water in the tank was 3150 cm^3.\r<BR>\n" );
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document.write( "the full capacity of the tank was 4200 cm^3.\r<BR>\n" );
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document.write( "that's what i get.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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