document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118558>Question 1118558</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A scientist has two solutions which she has labeled solution Aand solution B. Each contain salt. She knows that solution A is 70% salt and solution B is 95% salt. She wants to obtain 50 ounces of a mixture that is 90% salt.  How many ounces of each solution should she use ? </SPAN>\n" );
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document.write( "Yes; in the real world the problem as stated can't happen, because the salt percentages are not possible.<br><BR>\n" );
document.write( "However, you are not responsible for the fact that the problem that was given to you can't happen; the reason you asked the question was to get help learning how to solve the problem.<br><BR>\n" );
document.write( "Algebraically, the traditional approach is something like this....<br><BR>\n" );
document.write( "let x be the number of ounces of 70% solution; then (50-x) is the number of ounces of 95% solution.  You want x ounces of 70% solution combined with (50-x) ounces of 95% solution to give you 50 ounces of 90% solution.<br><BR>\n" );
document.write( "So write an equation saying that the total amount of salt in the two ingredients is equal to the amount of salt in the final mixture:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.70%28x%29+%2B+.95%2850-x%29+=+.90%2850%29 ALIGN=MIDDLE  ALT=\".70%28x%29+%2B+.95%2850-x%29+=+.90%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That equation can be solved with basic algebra; I leave it to you.<br><BR>\n" );
document.write( "But there is a much easier way to solve this kind of problem, if an algebraic solution is not required.<br><BR>\n" );
document.write( "The ratio in which the two ingredients have to be mixed is directly related to where the percentage of the mixture lies between the percentages of the two ingredients.<br><BR>\n" );
document.write( "The fastest way to explain how to solve your problem is this:<br><BR>\n" );
document.write( "\"The 90% target solution is 4/5 of the way from 70% to 95%; that means 4/5 of the mixture must be the 95% ingredient.\"<br><BR>\n" );
document.write( "Since 4/5 of 50 ounces is 40 ounces, that makes the answer 40 ounces of the 95% solution and 10 ounces of the 70% solution.<br><BR>\n" );
document.write( "Let's take a closer look at this method.<br><BR>\n" );
document.write( "Imagine you are starting with the 70% solution and adding the 95% solution.  The more of the 95% solution you add, the closer the percentage of the mixture comes to 95%.  If you add an equal amount of the 95% solution (so that 1/2 of the mixture is the 95% solution) then the percentage of the mixture will be halfway between 70% and 95%.  If you add 4 times as much of the 95% solution as you have 70% solution, then 4/5 of the mixture will be the 95% solution, and the percentage of the mixture will be 4/5 of the way from 70% to 95%.<br><BR>\n" );
document.write( "So, looking at the required calculations with the given percentages for your problem again, we see that from 70 to 95 is 25, and from 70 to 90 is 20; that means the fraction of the mixture that must be the 95% solution is 20/25 = 4/5. </SPAN>\n" );
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