Question

select the correct answer. michel owns a livestock trailer that can hold a maximum of 5,000 pounds. the average weight of each goat is 90 pounds, and the average weight of each calf is 360 pounds. michel would like to know how many goats and calves he can transport in a single trip. the inequality that represents this situation is graphed here. chart omitted a. michel can transport 42 goats and 2 calves in one trip b. michel can transport 30 goats and 8 calves in one trip c. michel can transport 24 goats and 10 calves in one trip d. michel can transport 50 goats and 4 calves in one trip

Explanation:

To solve this, we need to check which option satisfies the weight constraint: \( 90x + 360y \leq 5000 \), where \( x \) is the number of goats and \( y \) is the number of calves.

Step 1: Analyze Option A

• \( x = 42 \), \( y = 2 \)
• Calculate total weight: \( 90(42) + 360(2) = 3780 + 720 = 4500 \)
• \( 4500 \leq 5000 \): Valid, but let's check others.

Step 2: Analyze Option B

• \( x = 30 \), \( y = 8 \)
• Total weight: \( 90(30) + 360(8) = 2700 + 2880 = 5580 \)
• \( 5580 > 5000 \): Invalid.

Step 3: Analyze Option C

• \( x = 24 \), \( y = 10 \)
• Total weight: \( 90(24) + 360(10) = 2160 + 3600 = 5760 \)
• \( 5760 > 5000 \): Invalid.

Step 4: Analyze Option D

• \( x = 50 \), \( y = 4 \)
• Total weight: \( 90(50) + 360(4) = 4500 + 1440 = 5940 \)
• \( 5940 > 5000 \): Invalid.

Only Option A satisfies the weight limit.

Answer:

A. Michel can transport 42 goats and 2 calves in one trip