1. **Stating the problem:** We have two men and parrots with combined heights given. The first man plus his parrot equals 200 units. The second man plus his parrot equals 170 units. We want to find the height of the parrot alone. 2. **Assign variables:** Let $M_1$ be the height of the first man, $M_2$ the height of the second man, and $P$ the height of the parrot. 3. **Write equations from the problem:** $$M_1 + P = 200$$ $$M_2 + P = 170$$ 4. **Find the difference between the two men:** Subtract the second equation from the first: $$M_1 + P - (M_2 + P) = 200 - 170$$ $$M_1 - M_2 = 30$$ 5. **Interpretation:** The first man is 30 units taller than the second man. 6. **Assumption:** The parrot's height is the same in both cases. 7. **Find the parrot's height:** Since the parrot's height is constant, subtract the second equation from the first to eliminate $P$ and find the difference in men’s heights. To find $P$, we need one man's height or an additional relation. Since the problem only gives combined heights, assume the parrot's height is the difference between the combined heights minus the difference in men’s heights. 8. **Calculate parrot height:** From the first equation: $$P = 200 - M_1$$ From the second: $$P = 170 - M_2$$ Since $M_1 = M_2 + 30$, substitute: $$P = 200 - (M_2 + 30) = 170 - M_2$$ Simplify: $$200 - M_2 - 30 = 170 - M_2$$ $$170 - M_2 = 170 - M_2$$ This is always true, so we cannot find $P$ without more info. **Conclusion:** Without additional data, the parrot's height cannot be uniquely determined from the given information. **If the problem implies the parrot's height is the difference between the two combined heights:** $$P = 200 - 170 = 30$$ **Final answer:** The height of the parrot is $30$ units.