document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043905>Question 1043905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help:\r<BR>\n" );
document.write( "\n" );
document.write( "One canned juice drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10L  that is 7% orange juice? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659101 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let<BR>\n" );
document.write( "x = amount of the juice drink that is 15% orange juice<BR>\n" );
document.write( "y = amount of the juice drink that is 5% orange juice<BR>\n" );
document.write( "both amounts are in liters (L)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have x liters from one can and y liters from another can. We mix them together and together they make 10 liters of juice. So x+y = 10 is our first equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have x liters of the 15% orange juice. The amount of pure orange juice is 0.15x liters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have y liters of the 5% orange juice. The amount of pure orange juice is 0.05y liters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In total, those amounts combine to 0.15x+0.05y. We want 10 liters of 7% orange juice. So we want 10*0.07 = 0.7 liters of pure orange juice.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the two amounts must be the same (ie equal). So 0.15x+0.05y = 0.7 is the second equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To summarize so far, we have these two equations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y = 10<BR>\n" );
document.write( "0.15x+0.05y = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's focus on the first equation for now. Solve for y to get...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y-x = 10-x ... subtract x from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 10-x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that y is isolated, we can plug this into the other equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.15x+0.05y = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.15x+0.05( y ) = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.15x+0.05( 10-x ) = 0.7 ... replace y with 10-x. Now solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.15x+0.05(10)+0.05(-x) = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.15x+0.5-0.05x = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.10x+0.5 = 0.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.10x+0.5-0.5 = 0.7-0.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.10x = 0.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.10x/0.10 = 0.2/0.10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We finally know the value of x. Use this to find y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 10-x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 10-2 ... replace x with 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "----------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the end, we found that x = 2 and y = 8. Recall that at the very top we stated that\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = amount of the juice drink that is 15% orange juice<BR>\n" );
document.write( "y = amount of the juice drink that is 5% orange juice\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so this means that we must mix <font color=red size=4>2 liters</font> of the 15% juice drink with <font color=red size=4>8 liters</font> of the 5% juice drink.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );