1. **Stating the problem:** We have some bees and flowers. If each bee lands on a different flower, one bee does not get a flower. If two bees share each flower, there is one flower left out. We need to find the number of bees and flowers. 2. **Define variables:** Let $b$ be the number of bees and $f$ be the number of flowers. 3. **Translate conditions into equations:** - If each bee lands on a different flower, one bee does not get a flower. This means there are fewer flowers than bees by exactly one: $$f = b - 1$$ - If two bees share each flower, there is one flower left out. This means that when bees are paired two per flower, one flower remains unused: $$\frac{b}{2} = f - 1$$ 4. **Use the first equation to substitute $f$ in the second:** $$\frac{b}{2} = (b - 1) - 1$$ $$\frac{b}{2} = b - 2$$ 5. **Solve for $b$:** Multiply both sides by 2 to clear the fraction: $$2 \times \frac{b}{2} = 2 \times (b - 2)$$ $$\cancel{2} \times \frac{b}{\cancel{2}} = 2b - 4$$ $$b = 2b - 4$$ Subtract $2b$ from both sides: $$b - 2b = -4$$ $$-b = -4$$ Multiply both sides by $-1$: $$b = 4$$ 6. **Find $f$ using $f = b - 1$:** $$f = 4 - 1 = 3$$ **Final answer:** There are 4 bees and 3 flowers.