1. **State the problem:** Yasuhiko has invested 21355 in equipment and machinery. Each hummingbird feeder costs 12.75 to make and sells for 21.75. We need to find how many feeders he must sell to break even. 2. **Formula for break-even point:** The break-even point occurs when total revenue equals total cost. \[ \text{Total Revenue} = \text{Total Cost} \] 3. **Define variables:** Let $x$ be the number of feeders sold. - Total cost = fixed cost + variable cost = 21355 + 12.75x - Total revenue = selling price per feeder $ \times $ number sold = 21.75x 4. **Set up the equation:** $$ 21.75x = 21355 + 12.75x $$ 5. **Solve for $x$:** Subtract 12.75x from both sides: $$ 21.75x - 12.75x = 21355 $$ $$ 9x = 21355 $$ Divide both sides by 9: $$ x = \frac{21355}{9} = 2372.777\ldots $$ 6. **Interpretation:** Since Yasuhiko cannot sell a fraction of a feeder, he must sell at least 2373 feeders to break even. **Final answer:** $$ \boxed{2373} $$