SOLUTION: A pile of pennies, dimes, and half dollars (100 coins in all) is worth $5. How many dimes are in the pile?

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Question 460796: A pile of pennies, dimes, and half dollars (100 coins in all) is worth $5. How many dimes are in the pile?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let p = number of pennies
Let d = number of dimes
Let h = number of half dollars
given:
(1) +p+%2B+d+%2B+h+=+100+
(2) +1%2Ap+%2B+10d+%2B+50h+=+500+
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There are 2 equations and 3 unknowns, so
it is not directly solvable, but I can make
some logical conclusions.
(a)
The number of pennies is even and also
a multiple of +10+, otherwise, you
can't end up with a total of +500+.
(b)
You can't have +50+ dimes, since that
equals +500+.
(c)
The most dimes you could possibly have is
+40+, and then you have:
+50+ pennies = $.50
+40+ dimes = $4.00
+1+ half dollar = $.50
but then you only have +91+ coins
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Suppose you have 1 less dime. You have:
+60+ pennies = $.60
+39+ dimes = $3.90
+1+ half dollar = $.50
That adds up to +100+ coins and
must be the answer.