\begin{tabular}{l} You're printing shirts for your te zoomin \\ Master Ink charges a flat rate of \( \$ 35 \) \\ and \( \$ 5 \) per shirt. Totally Tee's charges \\ \( \$ 8 \) for each shirt and a flat rate of \( \$ 20 \). \\ \\ \hline Hint: Where do the two lines touch? \\ \hline Previous What is the break even point? \end{tabular}

To find the **break-even point** where the costs of **Master Ink** and **Totally Tee's** are the same, let's set up the equations based on their pricing structures. ### Given: - **Master Ink** - **Flat Rate:** \$35 - **Per Shirt Cost:** \$5 - **Total Cost (C₁):** \( C_1 = 35 + 5x \) - **Totally Tee's** - **Flat Rate:** \$20 - **Per Shirt Cost:** \$8 - **Total Cost (C₂):** \( C_2 = 20 + 8x \) Where \( x \) is the number of shirts ordered. ### Finding the Break-Even Point: Set the total costs equal to each other and solve for \( x \): \[ 35 + 5x = 20 + 8x \] 1. **Subtract \$20** from both sides: \[ 35 - 20 + 5x = 8x \] \[ 15 + 5x = 8x \] 2. **Subtract \( 5x \)** from both sides: \[ 15 = 3x \] 3. **Divide both sides by 3**: \[ x = 5 \] ### Conclusion: The **break-even point** occurs when ordering **5 shirts**. At this quantity: - **Master Ink's Total Cost:** \( 35 + (5 \times 5) = \$60 \) - **Totally Tee's Total Cost:** \( 20 + (8 \times 5) = \$60 \) Both companies charge **\$60** for **5 shirts**, meaning beyond this point, one may become more economical than the other depending on the number of shirts ordered.