document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102213>Question 1102213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Becky is doing research in which she needs 28 grams of a substance that is 30% protein. How many grams of each two ingredients, one that is 50% protein and the other 25% protein, should she mix together?<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 #716895 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The first tutor did indeed set up the problem incorrectly.<BR>\n" );
document.write( "The second tutor gave a perfectly good solution by the standard algebraic process.<br><BR>\n" );
document.write( "You can get the answer to mixture problems like this much faster and with much less effort using the method of alligation.  (Do an internet search on \"alligation\" if you want to learn more about this method.)<br><BR>\n" );
document.write( "Here is the diagram that is used to find the answer to your problem:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C3%2C25%2C%22%22%2C20%2C%22%22%2C30%2C%22%22%2C50%2C%22%22%2C5%29 ALIGN=MIDDLE  ALT=\"matrix%283%2C3%2C25%2C%22%22%2C20%2C%22%22%2C30%2C%22%22%2C50%2C%22%22%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In the left column, the entries are the percentages of the two ingredients, 25 and 50.<BR>\n" );
document.write( "In the middle column, the entry is the percentage of the mixture.<BR>\n" );
document.write( "The numbers in the right column are found by finding the differences, diagonally, between the numbers in the first two columns: 50-30=20, and 30-25=5.<br><BR>\n" );
document.write( "The numbers in the last column tell you the ratio in which the two ingredients must be mixed; the ratio of the 25% ingredient to the 50% ingredient needs to be 20:5, or 4:1.<br><BR>\n" );
document.write( "So 4/5 of the total 28 grams must be the 25% ingredient, and 1/5 must be the 50% ingredient.<br><BR>\n" );
document.write( "25% ingredient: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F5%29%2A28+=+112%2F5+=+22.4 ALIGN=MIDDLE  ALT=\"%284%2F5%29%2A28+=+112%2F5+=+22.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > grams<BR>\n" );
document.write( "50% ingredient: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29%2A28+=+28%2F5+=+5.6 ALIGN=MIDDLE  ALT=\"%281%2F5%29%2A28+=+28%2F5+=+5.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > grams<br><BR>\n" );
document.write( "Once you understand how to use this method, it is MUCH faster than the traditional algebraic approach.<BR>\n" );
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