document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288280>Question 288280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?\r<BR>\n" );
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document.write( "{maple syrup:  gallons, corn syrup: gallons}<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 #854254 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13334)</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=854254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The responses from the other tutors show setting up and solving the problem using the standard formal algebraic method.  That is of course a valid way to solve the problem.<br><BR>\n" );
document.write( "Any 2-part mixture problem like this can also be solved (quickly and easily if the numbers are \"nice\") using the fact that the ratio in which the two ingredients need to be mixed is exactly determined by where the unit price of the mixture lies between the prices of the two ingredients.<br><BR>\n" );
document.write( "Use a number line if it helps to observe/calculate that 2.36 is 1.56/5.20 = 156/520 = 3/10 of the way from 0.80 to 6.00.<br><BR>\n" );
document.write( "That means 3/10 of the mixture must be the more expensive ingredient.<br><BR>\n" );
document.write( "Since 50 gallons are to be made, the amount of maple syrup needed is (3/10)*50 = 15.<br><BR>\n" );
document.write( "ANSWERS: 15 gallons of maple syrup; 50-15 = 35 gallons of corn syrup<br><BR>\n" );
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