document.write( "Question 1185540: 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? \n" ); document.write( "

Algebra.Com's Answer #816380 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "Lawrence's wallet contains some ₱10.00, ₱5.00, ₱1.00, and ₱0.25 coins. There are 9 coins in his wallet.
\n" ); document.write( "How many of each type does he have if the wallet has a total of ₱20.50?
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document.write( "Definitely, there are at least two ₱0.25 coins.\r\n" );
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document.write( "Therefore, we can reformulate the problem equivalently by asking\r\n" );
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document.write( "    How many of each type does he have if the total money is  ₱20.00  and there are 7 coins, in all.\r\n" );
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document.write( "Next, there is at least one ₱10.00 coin, and it is clear that the number of ₱10.00 can not be two: it must be exactly one.\r\n" );
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document.write( "Therefore, we can reformulate the problem equivalently by asking\r\n" );
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document.write( "    How many of each type does he have if the total money is  ₱10.00  and there are 6 coins of ₱5.00 and/or ₱1.00.\r\n" );
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document.write( "Again, there is at least one ₱5.00 coin, and it is clear that the number of ₱5.00 can not be two: it must be exactly one.\r\n" );
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document.write( "So, finally, the answer is\r\n" );
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document.write( "    one ₱10.00 coin;  one ₱5.00 coin;  five ₱1.00 coins,  and two one ₱0.25 coins.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice, that from the linear algebra point of view, the problem allows only 2 equations for 4 unknowns;\r
\n" ); document.write( "\n" ); document.write( "but the requirement to have a solution in integer positive numbers leaves ONLY ONE possibility for the solution.\r
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