Mary had 15 coins in nickels and quarters. She had 3 more quarters than nickels.

To represent the situation with a system of equations, we need to set up two equations based on the information provided:

1. Total number of coins: Mary had 15 coins in total, which includes both nickels (x) and quarters (y). This gives us the first equation: \[ x + y = 15 \]

2. Relationship between nickels and quarters: Mary had 3 more quarters than nickels. This means: \[ y = x + 3 \]

Now, let's see how these equations match with the provided options.

Given two equations:

1. \( x + y = 15 \)
2. \( y = x + 3 \)

We can also express the second equation as \( y = 3 + x \), which means the equations can be rewritten.

Now, checking the options:

A) \[ x + y = 15 \] \[ y = 3 - x \]

B) \[ x + y = 3 \] \[ y = 15 + x \]

C) \[ x - y = 15 \] \[ y = 3 + x \]

D) \[ x + y = 15 \] \[ y = 3 + x \]

The correct option is: D) \[ x + y = 15 \] \[ y = 3 + x \]

Because we have both correct relationships as per the problem statement.