Maggie has 59 total coins for a total of $12.05. She only has quarters and dimes. How many of each coin does Maggie have?

Question

Responses
A 18 quarters and 41 dimes18 quarters and 41 dimes
B 50 quarters 9 dimes50 quarters 9 dimes
C 41 quarters and 18 dimes41 quarters and 18 dimes
D 9 quarters and 50 dimes

Answer 1

Let's denote the number of quarters as \( q \) and the number of dimes as \( d \).

We can set up the following equations based on the problem:

1. The total number of coins is 59: \[ q + d = 59 \]

2. The total value of the coins is $12.05, which is equivalent to 1205 cents. Since quarters are worth 25 cents and dimes are worth 10 cents, we can express this as: \[ 25q + 10d = 1205 \]

Now, we can solve these two equations.

From the first equation, we can express \( d \) in terms of \( q \): \[ d = 59 - q \]

Substituting \( d \) into the second equation: \[ 25q + 10(59 - q) = 1205 \]

Distributing the 10: \[ 25q + 590 - 10q = 1205 \]

Combining like terms: \[ 15q + 590 = 1205 \]

Subtracting 590 from both sides: \[ 15q = 615 \]

Dividing by 15: \[ q = 41 \]

Now we can find \( d \) using the first equation: \[ d = 59 - q = 59 - 41 = 18 \]

So Maggie has 41 quarters and 18 dimes.

Therefore, the answer is:

C: 41 quarters and 18 dimes.