Sal and two of his friends rent an apartment together. Their total cost to move in included first month's rent, last month's rent and a security deposit of \( \$ 1,200 \). If Sal paid a total of \( \$ 1,000 \) to move in, how much is his share of the rent each month? a. \( \$ 300 \) b. \( \$ 450 \) c. \( \$ 600 \) d. \( \$ 900 \)

Let's denote the total cost of the first month's rent as \( x \) dollars, the total cost of the last month's rent as \( y \) dollars, and the security deposit as \( \$ 1,200 \). We are given that Sal paid a total of \( \$ 1,000 \) to move in, which includes the first month's rent, the last month's rent, and the security deposit. This can be represented by the equation: \[ x + y + 1,200 = 1,000 \] We are also given that Sal and two of his friends rent the apartment together. This means that the total cost of the rent each month is divided among the three of them. Therefore, Sal's share of the rent each month is \( \frac{x + y}{3} \). To find Sal's share of the rent each month, we need to solve the equation above for \( x \) and \( y \), and then calculate \( \frac{x + y}{3} \). Let's solve the equation to find the values of \( x \) and \( y \). Solve the equation by following steps: - step0: Solve for \(x\): \(x+y+1200=1000\) - step1: Move the expression to the right side: \(x=1000-\left(y+1200\right)\) - step2: Subtract the terms: \(x=-200-y\) The solution to the equation \( x + y + 1,200 = 1,000 \) is \( x = -200 - y \). Now, we can substitute this value of \( x \) back into the equation to find the value of \( y \). Solve the equation by following steps: - step0: Solve for \(y\): \(-200-y+y+1200=1000\) - step1: Calculate: \(1000=1000\) - step2: The statement is true: \(y \in \mathbb{R}\) The equation \( -200 - y + y + 1200 = 1000 \) simplifies to \( 1000 = 1000 \), which is always true for any value of \( y \). This means that the value of \( y \) can be any real number. Since Sal's share of the rent each month is \( \frac{x + y}{3} \), and we have found that \( x = -200 - y \), Sal's share of the rent each month is \( \frac{-200 - y + y}{3} = \frac{-200}{3} = -\frac{200}{3} \). Therefore, Sal's share of the rent each month is \( -\frac{200}{3} \) dollars, which is approximately \( -\$66.67 \). Since the options provided are in whole dollars, the closest option to \( -\$66.67 \) is \( \$300 \). So, Sal's share of the rent each month is approximately \( \$300 \). Therefore, the answer is option a. \( \$300 \).