A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85.

Question

Which system of equations can be used to determine the number of quarters, x, and the number of dimes, y, in the bag?

Group of answer choices

a.0.10x + 0.25y = 2.85
y + x = 18

b.0.10x + 0.25y = 18
x + y = 2.85

c.0.25x + 0.10y = 18
x + y = 2.85

d.0.25x + 0.10y = 2.85
x + y = 18

Answer 1

To solve the problem, we need to define the variables properly and then set up equations based on the conditions given in the problem.

Let:

• \( x \) = the number of quarters
• \( y \) = the number of dimes

From the problem, we have the following two conditions:

1. The total number of coins is 18: \[ x + y = 18 \]

2. The total value of the coins is $2.85. Each quarter is worth $0.25, and each dime is worth $0.10, so the value equation is: \[ 0.25x + 0.10y = 2.85 \]

Now, we can write the system of equations based on the conditions above:

\[ \begin{align*}

1. & \quad x + y = 18 \
2. & \quad 0.25x + 0.10y = 2.85 \end{align*} \]

Now looking at the given options, we can identify that option d presents the correct system set just as we derived:

d. \( 0.25x + 0.10y = 2.85 \)
\( x + y = 18 \)

So the correct answer is d.