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Carlos has a box of coins that he uses when playing poker with friends. The Box currently contains 31 coins
consisting of pennies, dimes and quarters. The number of pennies is equal to the number of Dimes and the total value is $2.29.
How many of each denomination of coin does he have
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Let d = # of dimes and Q = # of quarters.
Notice that the number of pennies = d.
Then you have an equation for the number of coins
d + d + q = 31,
and the equation for the "value"
d + 10d + 25q = 229.
Thus you have a system
2d + q = 31, (1)
11d + 25q = 229. (2)
From (1), express q = 31-2d and substitute it into (2). You will get a single equation for q
11d + 25*(31-2d) = 229.
Simplify and solve it for d.
Then find q.
