document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145667>Question 1145667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have? </SPAN>\n" );
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document.write( "Using formal algebra....<br><BR>\n" );
document.write( "d = # of dimes<BR>\n" );
document.write( "q = # of quarters<br><BR>\n" );
document.write( "(1) 10d+25q = 620  [the value of the dimes (10 cents each) and quarters (25 cents each) is $6.20 = 620 cents]<BR>\n" );
document.write( "(2) d = 3q+18  [the number of dimes is 18 more than 3 times the number of quarters]<br><BR>\n" );
document.write( "Solve the pair of equations.  Probably the easiest method is to substitute (2) into (1) and solve for q; then use that value of q in either equation to solve for d.<br><BR>\n" );
document.write( "I leave it to you to get the practice finishing solving the problem using formal algebra.<br><BR>\n" );
document.write( "Using logical reasoning and simple mental arithmetic....<br><BR>\n" );
document.write( "(1) Count the 18 \"extra\" dimes.  Their value is 180 cents; that leaves 440 cents for the remaining coins.<BR>\n" );
document.write( "(2) The remaining coins are 3 dimes for each quarter.  Imagine the remaining coins in groups each consisting of 1 quarter and 3 dimes.  The value of 1 quarter and 3 dimes is 55 cents.<BR>\n" );
document.write( "(3) The number of groups at 55 cents each required to make the remaining 440 cents is 440/55 = 8.  In those 8 groups there are 8 quarters and 8*3=24 dimes.<BR>\n" );
document.write( "(4) So all together there are 8 quarters and 24+18=42 dimes.<br><BR>\n" );
document.write( " <BR>\n" );
document.write( "(3) The number of groups of </SPAN>\n" );
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