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Carlos has a box of coins that he uses when playing poker

with friends. The box currently contains 44 coins,
consisting of pennies, dimes, and quarters. The number of
pennies is equal to the number of dimes, and the total
value is $3.59. How many of each denomination of coin
does he have?

1 Answer

3 votes

Answer: hello person.

This is a system of equations problem that can be solved using substitution.

Let x be the number of pennies

Therefore the number of dimes is also x.

The number of quarters is 44 - 2x

The total value of the pennies is x * 0.01 = $0.01x

The total value of the dimes is x * 0.1 = $0.1x

The total value of the quarters is (44 - 2x) * 0.25 = $11 - 0.5x

Now we know that the total value is $0.01x + $0.1x + $11 - 0.5x = $3.59

So we can write the equation:

0.01x + 0.1x + 11 - 0.5x = 3.59

Now we can solve for x

0.6x + 11 = 3.59

0.6x = -7.41

x = -12.35

We know that x is the number of pennies and dimes. Since it is not a whole number, it is not possible.

We can think of another approach, assuming that x is the number of dimes and pennies, and y is the number of quarters.

x + y = 44

0.1x + 0.25y = 3.59

Now we can solve for x and y by substitution method.

x = 44 - y

0.1(44 - y) + 0.25y = 3.59

4.4 - 0.1y + 0.25y = 3.59

4.4 = 0.35y + 3.59

0.81 = 0.35y

y = 2.3

x = 44 - 2.3 = 41.7

We know that x and y must be whole numbers. Since x and y are not whole numbers it is not possible.

Hence, there is no possible number of coins for Carlos to have for the given scenario.

Explanation:

User Jopke
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