Set 12: Systems of Equations (Advanced)

Explanation

Answer: B

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)

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

✓ Correct

12 horses

14 horses

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Let $h$ = horses and $c$ = chickens. System: $\begin{cases} h + c = 22 \\ 4 h + 2 c = 64 \end{cases}$ Step 1: From first: $c = 22 - h$ Step 2: Substitute: $$$4h + 2(22 - h) = 64 $4h + 44 - 2 h = 64$ 2h = 20 $h = 10$$ 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.

Key Steps:

•

The correct answer is 10 horses

Why others are wrong:

A: Choice A is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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