document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185540>Question 1185540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lawrence's wallet contains some ₱10.00, ₱5.00, ₱1.00, and ₱0.25 coins. There are 9 coins in his wallet. How many of each type does he have if the wallet has a total of ₱20.50? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816366 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A pure mathematical solution to this problem would be very complex; however, there are many ways to solve this easily using logical reasoning.<br><BR>\n" );
document.write( "You will learn nothing from this, and get no valuable mental exercise, if we simply show you the answer, or even if we show you the complete solution process.<br><BR>\n" );
document.write( "I will instead suggest a few ways you can start on the problem and let you finish.  To get the most benefit, try finishing the solution from each of the starts I show.<br><BR>\n" );
document.write( "(1) A \"greedy\" approach -- starting with the highest value coins....<br><BR>\n" );
document.write( "We can't have two ₱10 coins, because that would make ₱20, and we would have only ₱0.50 to make with the remaining 7 coins.  So we can only have one ₱10 coin.<BR>\n" );
document.write( "That leaves ₱10.50 to make with the other 8 coins.<BR>\n" );
document.write( "A similar analysis then shows we can only have one ₱5 coin.<br><BR>\n" );
document.write( "...then continue from there....<br><BR>\n" );
document.write( "(2) Using the fact that only the ₱0.25 coins have values that are fractions....<br><BR>\n" );
document.write( "With a total of ₱20.50, the number of ₱0.25 coins must be either 2 (to make ₱0.50) or 6 (to make ₱1.50). Quick analysis shows there can't be 6 ₱0.25 coins, because that would leave only 3 coins to make the remaining ₱19.  So the number of ₱0.25 coins has to be 2.<br><BR>\n" );
document.write( "... and again continue from there....<br><BR>\n" );
document.write( "(3) Using the assumption that the statement of the problem implies that he has at least one of each coin....<br><BR>\n" );
document.write( "1 of each coin make a total value of ₱16.25, leaving 5 more coins to make the remaining ₱4.25.  Obviously one of the remaining coins has to be another ₱0.25 coin....<br><BR>\n" );
document.write( "... and then continue on that path....<br><BR>\n" );
document.write( " </SPAN>\n" );
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