document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132883>Question 1132883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers whose sum is <BR>\n" );
document.write( "70 and whose difference is <BR>\n" );
document.write( "18. </SPAN>\n" );
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document.write( "This kind of system of equations comes up in a large number of very different kinds of problems: the sum of two numbers is x and their difference is y; what are the two numbers.<br><BR>\n" );
document.write( "Solving the problem using formal algebra is of course valid; and you should know how to set up and solve a problem like this using formal algebra.  But there is a quick path to the answer to this kind of problem using logical reasoning and simple mental arithmetic.<br><BR>\n" );
document.write( "Think of the operations of adding a second number to a first number, and subtracting that same second number from the first number, on a number line.<br><BR>\n" );
document.write( "You start at the first number; to add the second number you go one direction on the number line, and to subtract the second number you go the opposite direction.<br><BR>\n" );
document.write( "That means the first number is halfway between the two places you end up, which are the sum and difference of the two numbers.<br><BR>\n" );
document.write( "So the first number is just the average of the sum and difference of the two numbers; then the second number is the distance from the first number to either the sum or difference.<br><BR>\n" );
document.write( "For this example....<br><BR>\n" );
document.write( "sum = 70; difference = 18  -->  average is (70+18)/2 = 44<br><BR>\n" );
document.write( "So one of the numbers is 44; the other is 70-44 = 26, or 44-18 = 26.  </SPAN>\n" );
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