document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135345>Question 1135345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An engine has a 4.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 55.1 % solution (a mix of 55.1 % pure antifreeze and 44.9 % water). How much pure antifreeze (in litres) must be combined with a 45.4 % solution to achieve 4.6 litres of the ideal solution? <BR>\n" );
document.write( "Express your answer to three significant digits. </SPAN>\n" );
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document.write( "Using the traditional algebraic method for solving the problem, write an equation that says x liters of pure (100%) antifreeze must be added to (4.6-x) liters of 45.4% antifreeze to get 4.6 liters of 55.1% antifreeze:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28x%29%2B.454%284.6-x%29+=+.551%284.6%29 ALIGN=MIDDLE  ALT=\"1%28x%29%2B.454%284.6-x%29+=+.551%284.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <--- corrected equation, thanks tutor @ikleyn; I previously showed .0454 and .0551....<br><BR>\n" );
document.write( "Ugly numbers; I'll let you finish the solution by that method.<br><BR>\n" );
document.write( "Here is a MUCH easier way to get the answer to a problem like this, based on the concept that the ratio in which the two ingredients need to be mixed is directly related to where the target percentage of 55.1% lies between the 45.4% and 100% percentages of the ingredients.<br><BR>\n" );
document.write( "Here without detailed explanation are the required calculations for your problem.<br><BR>\n" );
document.write( "(1) 55.1-45.4 = 9.7; 100-45.4 = 54.6<BR>\n" );
document.write( "(2) 9.7/54.6 = 0.177655678... is the fraction of the way that 55.1% is from 45.4% to 100%, so it is the fraction of the mixture that needs to be the higher percentage ingredient<BR>\n" );
document.write( "(3) 0.177688678*4.6 = 0.817216... is the number of liters of pure antifreeze that must be used in the mixture.<br><BR>\n" );
document.write( "ANSWER (to 3 significant digits): 0.817 liters </SPAN>\n" );
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