You're printing shirts for your te zoomm 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 \( \$ 20 \). 8. What is the break even point? Hint: Where do the two lines touch? Type a response Previous 2 of 3 Next \( \rightarrow \)

To find the **break-even point** where both printing companies charge the same total cost, let's set up the cost equations for each company and solve for the number of shirts \( x \). ### Cost Equations: 1. **Master Ink** - **Flat Rate:** \$35 - **Per Shirt:** \$5 - **Total Cost:** \( C_1(x) = 35 + 5x \) 2. **Totally Tee** - **Flat Rate:** \$20 - **Per Shirt:** \$8 - **Total Cost:** \( C_2(x) = 20 + 8x \) ### Setting the Costs Equal: To find the break-even point, set \( C_1(x) \) equal to \( C_2(x) \): \[ 35 + 5x = 20 + 8x \] ### Solving for \( x \): 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 printing **5 shirts**. At this quantity, both Master Ink and Totally Tee charge the same total cost. - **Master Ink Cost:** \( 35 + (5 \times 5) = \$60 \) - **Totally Tee Cost:** \( 20 + (8 \times 5) = \$60 \) Both companies charge \$60 for printing 5 shirts, confirming the break-even point. **Answer:** The break-even point occurs when printing 5 shirts.