document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251219>Question 251219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dairy farmer had 54 liters of milk in 3 churns. He wanted to make sure each churn contained 18 liters. First, he poured 1/4 of the firs churn into the second churn. Then he poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn. How many liters did each churn contain before he started pouring? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184143 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A dairy farmer had 54 liters of milk in 3 churns.<BR>\n" );
document.write( " He wanted to make sure each churn contained 18 liters. <BR>\n" );
document.write( "First, he poured 1/4 of the firs churn into the second churn.<BR>\n" );
document.write( " Then he poured 1/2 of the second churn into the third churn.<BR>\n" );
document.write( " Finally, he poured 1/3 of the third churn into the first churn.<BR>\n" );
document.write( " How many liters did each churn contain before he started pouring?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x, y, z = the amts in each churn originally<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"A dairy farmer had 54 liters of milk in 3 churns.\"<BR>\n" );
document.write( "x + y + z = 54<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"he poured 1/4 of the first churn into the second churn.<BR>\n" );
document.write( "then<BR>\n" );
document.write( "1st churn = .75x<BR>\n" );
document.write( "2nd churn =  (y+.25x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Then he poured 1/2 of the second churn into the third churn.\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2nd churn = .5(y+.25x) = (.5y+.125x)<BR>\n" );
document.write( "3rd churn = z+.5y+.125x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" he poured 1/3 of the third churn into the first churn.\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3rd churn = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(z+.5y+ .125x)<BR>\n" );
document.write( "1st churn = .75x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(z+.5y+.125x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "At this point we assume all churns = 18 gal<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1st churn<BR>\n" );
document.write( ".75x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(z+.5y+.125x) = 18<BR>\n" );
document.write( "Multiply by 3:<BR>\n" );
document.write( "2.25x + z + .5y + .125x = 54<BR>\n" );
document.write( "2.375x + .5y + z = 54<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2nd churn<BR>\n" );
document.write( ".5y + .125x = 18<BR>\n" );
document.write( ".125x + .5y = 18<BR>\n" );
document.write( ".5y = 18 - .125x<BR>\n" );
document.write( "multiply by 2, can use this for substitution<BR>\n" );
document.write( "y = (36 - .25x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3rd churn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(z+.5y+ .125x) = 18<BR>\n" );
document.write( "multiply by 3<BR>\n" );
document.write( "2(z+.5y + .125x) = 54<BR>\n" );
document.write( "2z + y + .25x = 54<BR>\n" );
document.write( ".25x + y + 2z = 54<BR>\n" );
document.write( "Replace y with (36-.25x)<BR>\n" );
document.write( ".25x + (36-.25x) + 2z = 54<BR>\n" );
document.write( ".25x - .25x + 2z = 54 - 36; (x is conveniently eliminated)<BR>\n" );
document.write( "2z = 18<BR>\n" );
document.write( "z = 9 gal originally<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the total equation<BR>\n" );
document.write( "x + y + 9 = 54<BR>\n" );
document.write( "x + y = 54 - 9<BR>\n" );
document.write( "x + y = 45<BR>\n" );
document.write( "we also know, (use these two equation for elimination)<BR>\n" );
document.write( ".125x + .5y = 18<BR>\n" );
document.write( "Multiply by 2, subtract x + y = 45<BR>\n" );
document.write( ".25x + y = 36<BR>\n" );
document.write( " x +   y = 45<BR>\n" );
document.write( "-----------------subtraction eliminates y<BR>\n" );
document.write( "-.75x = -9<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%2F%28-.75%29 ALIGN=MIDDLE  ALT=\"%28-9%29%2F%28-.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 12 gal originally<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12 + y + 9 = 54<BR>\n" );
document.write( "y = 54 - 21<BR>\n" );
document.write( "y = 33 gal originally<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that works<BR>\n" );
document.write( "\"he poured 1/4 of the first churn into the second churn.<BR>\n" );
document.write( "then<BR>\n" );
document.write( "1st churn has 9 gal<BR>\n" );
document.write( "2nd churn has 36 gal<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"poured 1/2 of the second churn into the third churn.\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2nd churn has 18 gal<BR>\n" );
document.write( "3rd churn has 27 gal<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" he poured 1/3 of the third churn into the first churn.\"<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3rd churn = 18<BR>\n" );
document.write( "1st churn = 18<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( " How many liters did each churn contain before he started pouring?<BR>\n" );
document.write( "x = 12; y = 33, z = 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Merry Christmas, hope this made sense!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );