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

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) (Show Source): You can put this solution on YOUR website!
Let = number of pennies
Let = number of dimes
Let = number of half dollars
given:
(1)
(2)
-----------------------------
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 , otherwise, you
can't end up with a total of .
(b)
You can't have dimes, since that
equals .
(c)
The most dimes you could possibly have is
, and then you have:
pennies = $.50
dimes = $4.00
half dollar = $.50
but then you only have coins
------------------------------------------
Suppose you have 1 less dime. You have:
pennies = $.60
dimes = $3.90
half dollar = $.50
That adds up to coins and
must be the answer.

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