document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193922>Question 1193922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marge purchased x bicycle helmets and y tire pumps.  Each helmet cost $15.00 and each pump cost $7.00.  She purchased a total of 21 items and spent $243.00.  How many helmets did Marge buy? </SPAN>\n" );
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document.write( "A setup for solving the problem using formal algebra....<br><BR>\n" );
document.write( "x+y=21  (the total number of items was 21)<BR>\n" );
document.write( "15x+7y=243  (the total cost was $243)<br><BR>\n" );
document.write( "With the two equations in that form, I would solve using elimination:<br><BR>\n" );
document.write( "7x+7y=147  (first equation, multiplied by 7)<BR>\n" );
document.write( "15x+7y=243<BR>\n" );
document.write( "8x=96  (difference between the two equations)<br><BR>\n" );
document.write( "I'll let you finish; it's basic algebra.<br><BR>\n" );
document.write( "An informal solution, using logical reasoning and mental arithmetic (which gives you better mental exercise than using formal algebra....):<br><BR>\n" );
document.write( "The cost of each helmet is $15, which is a multiple of $5; so the total cost of the helmets will be a multiple of $5 -- i.e., the units digit of the total cost of the helmets is either 5 or 0.<BR>\n" );
document.write( "Since the total cost of all the items has units digit 3, the total cost of the pumps at $7 each must be either 3 or 8.  So the possible numbers of pumps are 4, 9, 14, or 19.<br><BR>\n" );
document.write( "Try each possibility to see which one satisfies all the conditions of the problem.<br><BR>\n" );
document.write( " </SPAN>\n" );
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