Question 4 Answer & Explanation - SAT Algebra

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algebra

A stable has horses and rabbits. There are 22 animals with 64 legs. How many horses are there? (Horses have 4 legs, rabbits have 4 legs)

Wait, both have 4 legs, so this won't work. Let me change to horses and chickens.

A stable has horses and chickens. There are 22 animals with 64 legs. How many horses are there? (Horses have 4 legs, chickens have 2 legs)

8 horses

10 horses

12 horses

14 horses

Choice B is the correct answer. Let $h$ = horses and $c$ = chickens.

System: $\begin{cases} h + c = 22 \\ 4h + 2c = 64 \end{cases}$

Step 1: From first: $c = 22 - h$

Step 2: Substitute: $4h + 2(22 - h) = 64$ $4h + 44 - 2h = 64$ $2h = 20$ $h = 10$

Solution: 10 horses (and 12 chickens)

Verification: $10 + 12 = 22$ ✓ and $4(10) + 2(12) = 40 + 24 = 64$ ✓

💡 Strategic Tip: Different leg counts create solvable systems.

**Other choices fail verification.