4) Rory sold T-shirts at a festival for \( \$ 15 \) each. He paid \( \$ 100 \) in materials and fees. Rory's profit after the festival was \( \$ 350 \). He wants to know how many shirts he sold. \( \begin{array}{ll}\text { (4) Which quantity is unknown? } \\ \)\begin{tabular}{ll}\hline \text { (4) the price of each shirt } & \text { (4) the cost of materials and fees } \\ \hline \text { (4) the profit after the festival } \\ \hline\end{tabular}\end{array}\( . \begin{array}{l}\text { (4) }\end{array} \)

To determine the unknown quantity in Rory's situation, let's analyze the information provided: 1. **Price of each T-shirt**: \( P = 15 \) 2. **Cost of materials and fees**: \( C = 100 \) 3. **Profit after the festival**: \( \text{Profit} = 350 \) The profit can be calculated using the formula: \[ \text{Profit} = \text{Revenue} - \text{Cost} \] Where: - Revenue is the total income from selling the T-shirts. - Cost is the total expenses (materials and fees). Let \( N \) be the number of T-shirts sold. The revenue from selling \( N \) T-shirts is given by: \[ \text{Revenue} = P \times N = 15N \] Now, substituting the known values into the profit formula: \[ 350 = 15N - 100 \] Now, we can solve for \( N \): 1. Add \( 100 \) to both sides: \[ 350 + 100 = 15N \] \[ 450 = 15N \] 2. Divide both sides by \( 15 \): \[ N = \frac{450}{15} \] Now, let's calculate \( N \). Calculate the value by following steps: - step0: Calculate: \(\frac{450}{15}\) - step1: Reduce the numbers: \(\frac{30}{1}\) - step2: Calculate: \(30\) After performing the calculation, we find that: \[ N = 30 \] This means Rory sold **30 T-shirts** at the festival. ### Summary of Unknown Quantity: - The unknown quantity in this problem is the **number of T-shirts sold**, which we calculated to be **30**. ### Conclusion: Rory sold **30 T-shirts** to achieve a profit of **$350** after covering his costs.