1. Problem 1: Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet. How many of each animal does he have? 2. Step 1: Understand the problem. - Total animals: $250$ - Total feet: $760$ - Chickens have 2 feet each, goats have 4 feet each. 3. Step 2: Devise a plan. - Let $c$ = number of chickens, $g$ = number of goats. - We have two equations: $$c + g = 250$$ $$2c + 4g = 760$$ 4. Step 3: Carry out the plan. - From the first equation, $c = 250 - g$. - Substitute into the second equation: $$2(250 - g) + 4g = 760$$ $$500 - 2g + 4g = 760$$ $$2g = 760 - 500$$ $$2g = 260$$ $$g = 130$$ - Then, $c = 250 - 130 = 120$. 5. Step 4: Review/Check. - Total feet check: $2(120) + 4(130) = 240 + 520 = 760$ correct. 6. Strategies used: Algebraic substitution and equation system solving. 7. Problem 2: One number is 3 less than another number. If the sum of the two numbers is 177, find each number. 8. Step 1: Understand the problem. - Let the two numbers be $x$ and $y$. - Given: $x = y - 3$ and $x + y = 177$. 9. Step 2: Devise a plan. - Substitute $x$ in the sum equation. 10. Step 3: Carry out the plan. - Substitute $x = y - 3$ into $x + y = 177$: $$(y - 3) + y = 177$$ $$2y - 3 = 177$$ $$2y = 180$$ $$y = 90$$ - Then, $x = 90 - 3 = 87$. 11. Step 4: Review/Check. - Sum check: $87 + 90 = 177$ correct. 12. Strategies used: Substitution and equation solving. Final answers: - Problem 1: Chickens = 120, Goats = 130. - Problem 2: Numbers are 87 and 90.