document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615814>Question 615814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A yogurt company blends regular yogurt that is 4% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of non-fat yogurt must be mixed to obtain 60 pounds of low-fat yogurt? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387321 by </B><A HREF=/tutors/aboutme.mpl?userid=dragonwalker><B>dragonwalker(73)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dragonwalker><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=387321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (note * symbol used for multiplication sign so as not to confuse the algebra unit x)\r<BR>\n" );
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document.write( "Firstly you want to look at what you know. <BR>\n" );
document.write( "1) There will be a final product of 60lbs of yogurt<BR>\n" );
document.write( "2) There are two types of yogurt, one that is 0% fat and the other 4% (which can also be written as 0.04 (4/100)\r<BR>\n" );
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document.write( "The 4% fat has a greater amount of fat than the final product of 1% (+3)<BR>\n" );
document.write( "The 0% fat has a lesser amount of fat than the final product of 1% (-1)\r<BR>\n" );
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document.write( "So for every unit of 4% we need to lower it by 3 to get the 1%.<BR>\n" );
document.write( "How can we lower it by 3? Well one unit of 0% fat would lower by one (-1), so 3 units of 0% would lower it by 3?\r<BR>\n" );
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document.write( "So for 1 unit of 4% we need to add 3 units of 0% (a total of 4).<BR>\n" );
document.write( "So now we need to see how big one of these units is. <BR>\n" );
document.write( "We need a total of 4 units to mix the yogurt correctly so we need to see how many times 4 goes into 60 lbs. Let us say that x is the size of one unit so:\r<BR>\n" );
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document.write( "4x = 60<BR>\n" );
document.write( "x = 60/4<BR>\n" );
document.write( "x = 15\r<BR>\n" );
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document.write( "so each unit is 15 lbs\r<BR>\n" );
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document.write( "So how many units of 4% did we need? 1 unit (or 1x).\r<BR>\n" );
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document.write( "so: 1x = 1 * 15<BR>\n" );
document.write( "       = 15 lbs<BR>\n" );
document.write( "How much 0% did we need? 3 units.\r<BR>\n" );
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document.write( "So 3 units  (or 3x) = 3 * 15<BR>\n" );
document.write( "           = 45\r<BR>\n" );
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document.write( "So we need 45 lbs of 0%\r<BR>\n" );
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document.write( "So we need 15 lbs of 4% and 45 lbs of 0%\r<BR>\n" );
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document.write( "To check:\r<BR>\n" );
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document.write( "we know x = 15\r<BR>\n" );
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document.write( "so if we decide to multiply the amounts with the concentrations then we should end up with a balanced equation.\r<BR>\n" );
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document.write( "How much fat in 60 lbs of 1 %?\r<BR>\n" );
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document.write( "1 % is one hundredth or 1/100 = 0.01<BR>\n" );
document.write( "so the amount of fat is 60 * 0.01 = 0.6 lbs of fat\r<BR>\n" );
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document.write( "4% is 4/100 = 0.04\r<BR>\n" );
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document.write( "So 0.04 * 15 = 0.6 lbs of fat!!! <BR>\n" );
document.write( "The 0% yogurt doesn't add any fat, but just makes the weight up to 60 lbs.\r<BR>\n" );
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document.write( "However although finding out how much fat you need in the final product and then working out how to get that amount of fat using the 4% would work for this, the other method is needed if both yogurts being mixed have some fat. \r<BR>\n" );
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