document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209500>Question 1209500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Containers A B and C contained water. 1/5  was poured from A to B. 1/6 of the water from B was then poured into C. Finally 1/6 was transferred from C to A. In the end there were 8.5 litres of water in each container. How much water was there in B  at first. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848936 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the initial amounts of water in containers \( A \), \( B \), and \( C \) be \( a \), \( b \), and \( c \) liters, respectively. \r<BR>\n" );
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document.write( "### Step 1: Transfer water from \( A \) to \( B \)<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Amount poured from } A \text{ to } B = \frac{1}{5}a<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "After this transfer:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "A = a - \frac{1}{5}a = \frac{4}{5}a, \quad B = b + \frac{1}{5}a<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "### Step 2: Transfer water from \( B \) to \( C \)<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Amount poured from } B \text{ to } C = \frac{1}{6}(b + \frac{1}{5}a)<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "After this transfer:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "B = b + \frac{1}{5}a - \frac{1}{6}(b + \frac{1}{5}a) = b + \frac{1}{5}a - \frac{1}{6}b - \frac{1}{30}a<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "C = c + \frac{1}{6}(b + \frac{1}{5}a)<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "### Step 3: Transfer water from \( C \) to \( A \)<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Amount poured from } C \text{ to } A = \frac{1}{6}[c + \frac{1}{6}(b + \frac{1}{5}a)]<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "After this transfer:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "C = c + \frac{1}{6}(b + \frac{1}{5}a) - \frac{1}{6}[c + \frac{1}{6}(b + \frac{1}{5}a)]<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "A = \frac{4}{5}a + \frac{1}{6}[c + \frac{1}{6}(b + \frac{1}{5}a)]<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "### Step 4: Final state<BR>\n" );
document.write( "At the end, all containers have the same amount of water: \( 8.5 \) liters.\r<BR>\n" );
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document.write( "#### Equations:<BR>\n" );
document.write( "1. \( A = 8.5 \):<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   \frac{4}{5}a + \frac{1}{6}[c + \frac{1}{6}(b + \frac{1}{5}a)] = 8.5<BR>\n" );
document.write( "   \]<BR>\n" );
document.write( "2. \( B = 8.5 \):<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   b + \frac{1}{5}a - \frac{1}{6}(b + \frac{1}{5}a) = 8.5<BR>\n" );
document.write( "   \]<BR>\n" );
document.write( "3. \( C = 8.5 \):<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   c + \frac{1}{6}(b + \frac{1}{5}a) - \frac{1}{6}[c + \frac{1}{6}(b + \frac{1}{5}a)] = 8.5<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "We will solve the system of equations to find \( b \), the initial amount of water in container \( B \).\r<BR>\n" );
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document.write( "The initial amount of water in container \( B \) was \( \mathbf{8.5 \, \text{liters}} \). It turns out that all three containers started with the same amount of water, \( 8.5 \) liters. </SPAN>\n" );
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