1. **State the problem:** A company makes first-aid kits with fabric and plastic bandages in a ratio of 3 to 9. A small kit has 16 fabric bandages. We need to find how many plastic bandages are in the small kit. 2. **Understand the ratio:** The ratio of fabric to plastic bandages is 3:9. This means for every 3 fabric bandages, there are 9 plastic bandages. 3. **Set up the proportion:** Let $x$ be the number of plastic bandages in the small kit. Since the ratio must be the same, we have: $$\frac{\text{fabric}}{\text{plastic}} = \frac{3}{9} = \frac{16}{x}$$ 4. **Solve for $x$:** Cross-multiply: $$3 \times x = 9 \times 16$$ $$3x = 144$$ 5. **Divide both sides by 3:** $$\cancel{3}x = \frac{144}{\cancel{3}}$$ $$x = 48$$ 6. **Answer:** The small kit has 48 plastic bandages.