Question 1185540
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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?
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Definitely, there are at least two ₱0.25 coins.


Therefore, we can reformulate the problem equivalently by asking

    How many of each type does he have if the total money is  ₱20.00  and there are 7 coins, in all.




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.


Therefore, we can reformulate the problem equivalently by asking

    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.




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.


So, finally, the answer is


    one ₱10.00 coin;  one ₱5.00 coin;  five ₱1.00 coins,  and two one ₱0.25 coins.
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Solved.


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Notice, that from the linear algebra point of view, the problem allows only 2 equations for 4 unknowns;

but the requirement to have a solution in integer positive numbers leaves ONLY ONE possibility for the solution.