Two friends decide to rent an apartment and split the cost evenly. They each paid \( \$ 575 \) towards the total move in cost of first and last month's rent and a security deposit. If the apartment cost \( \$ 325 \) per month to rent, how much was the security deposit? a. \( \$ 125 \) b. \( \$ 250 \) c. \( \$ 500 \) d. \( \$ 825 \)

To find the security deposit, we first need to calculate the total move-in cost, which includes the first month's rent, the last month's rent, and the security deposit. 1. **Calculate the total rent for the first and last month:** \[ \text{First month's rent} = \$ 325 \] \[ \text{Last month's rent} = \$ 325 \] \[ \text{Total rent for first and last month} = 325 + 325 = \$ 650 \] 2. **Calculate the total amount paid by both friends:** Each friend paid \( \$ 575 \), so together they paid: \[ \text{Total amount paid} = 575 + 575 = \$ 1150 \] 3. **Set up the equation for the total move-in cost:** The total move-in cost consists of the total rent for the first and last month plus the security deposit (let's denote the security deposit as \( x \)): \[ 650 + x = 1150 \] 4. **Solve for the security deposit \( x \):** \[ x = 1150 - 650 \] \[ x = 500 \] Thus, the security deposit is \( \$ 500 \). The answer is \( \boxed{500} \).