document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155750>Question 1155750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A​ sparkling-water distributor wants to make up 400 gal of sparkling water to sell for $ 8.00 per gallon. She wishes to mix three grades of water selling for ​$14​.00, ​$3​.00, and​ $4.50 per​ gallon, respectively. She must use twice as much of the​ $4.50 water as the $ 3.00 comma water. How many gallons of each should she​ use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778429 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=778429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If you solve the problem using formal algebra, then certainly use a single variable -- it is MUCH less work.<br><BR>\n" );
document.write( "I solve this kind of problem informally, if I can.  The numbers in this problem make it easy; being good with mental arithmetic, I solved the problem in about 15 seconds.<br><BR>\n" );
document.write( "Work with two ingredients at a time, as follows....<br><BR>\n" );
document.write( "The mixture uses twice as much $4.50 water as $3 water.  That means the average price of those two ingredients is \"twice as close to $4.50 as it is to $3\"; that makes the average cost of those two ingredients $4.<br><BR>\n" );
document.write( "Now the problem is to mix $4 water and $14 water to get $8 water.<br><BR>\n" );
document.write( "$8 is 4/10=2/5 of the way from $4 to $14; that means 2/5 of the total mixture is the $14 water.<br><BR>\n" );
document.write( "So 2/5 of the 400 gallons, or 160 gallons, is the $14 water.<br><BR>\n" );
document.write( "That leaves 240 gallons of the $3 water and $4.50 water.  Since the amount of $4.50 water is twice the amount of $3 water, that means 160 gallons of the $4.50 water and 80 gallons of the $3 water.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "160 gallons of $14 water<BR>\n" );
document.write( "160 gallons of $4.50 water<BR>\n" );
document.write( "80 gallons of $3 water<br><BR>\n" );
document.write( " </SPAN>\n" );
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