document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185429>Question 1185429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this <BR>\n" );
document.write( "How many ounces of 1% antifreeze solution must be added to 100 oz of 40% antifreeze solution to obtain a 16% antifreeze solution?\r<BR>\n" );
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document.write( "Thank you so much<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816249 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=816249\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of ounces of 1% solution.<BR>\n" );
document.write( "let y = total number of ounces of 16% solution.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( ".01x + .4*100 = .16y<BR>\n" );
document.write( "x + 100 = y\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".01x + 40 = .16y<BR>\n" );
document.write( "x + 100 = y\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 100 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "x + 4000 = 16y<BR>\n" );
document.write( "x + 100 = y\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "3900 = 15y\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 3900 / 15 = 260\r<BR>\n" );
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document.write( "confirm that your original equations are correct when you replace y with 260.\r<BR>\n" );
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document.write( "the original equations are:\r<BR>\n" );
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document.write( ".01x + .4*100 = .16y<BR>\n" );
document.write( "x + 100 = y\r<BR>\n" );
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document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
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document.write( ".01x + 40 = .16y<BR>\n" );
document.write( "x + 100 = y\r<BR>\n" );
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document.write( "replace y with 260 to get:\r<BR>\n" );
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document.write( ".01x + 40 = .16*260<BR>\n" );
document.write( "x + 100 = 260\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".01x + 40 = 41.6<BR>\n" );
document.write( "x + 100 = 260\r<BR>\n" );
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document.write( "subtract 40 from both sides of the first equation and subtract 100 from both sides of the second equation to get:\r<BR>\n" );
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document.write( ".01x = 41.6 - 40<BR>\n" );
document.write( "x = 260 - 100\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".01x = 1.6<BR>\n" );
document.write( "x = 160\r<BR>\n" );
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document.write( "go back to your original equations and replace y with 260 and x with 160 to get:\r<BR>\n" );
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document.write( ".01x + 40 = .16y becomes 1.6 + 40 = .16 * 260<BR>\n" );
document.write( "x + 100 = y becomes 160 + 100 = 260\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "41.6 = 41.6<BR>\n" );
document.write( "260 = 260\r<BR>\n" );
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document.write( "this confirms the values of x and y are correct.\r<BR>\n" );
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document.write( "your solution is that:\r<BR>\n" );
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document.write( "x = 160 and y = 260\r<BR>\n" );
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document.write( "let x = the number of ounces of 1% solution.<BR>\n" );
document.write( "let y = total number of ounces of 16% solution.\r<BR>\n" );
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document.write( "this means that 160 ounces of 1% solution are added to 100 ounces of 40% solution to get 260 ounces of 16% solution.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "normally you would want to move all the variables to the left side of the equal sign and all the constants to the right side of the equal sign, but this is not necessary, and in this case, it was preferable to leave them where they were.\r<BR>\n" );
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