Question
Jared wants to build a square pen in front of the chicken coop for his chickens. He has a 140-foot roll of fencing wire to use. Jared can use all of the fencing wire, but he does not have to.
If x = the side length of the square pen, which model and inequality correctly represent this problem?
Responses
A
4x < 140
Image with alt text: 4 x < 140
B
4x > 140
Image with alt text: 4 x > 140
C
4x < 140
Image with alt text: 4 x < 140
D
x + 4 <
If x = the side length of the square pen, which model and inequality correctly represent this problem?
Responses
A
4x < 140
Image with alt text: 4 x < 140
B
4x > 140
Image with alt text: 4 x > 140
C
4x < 140
Image with alt text: 4 x < 140
D
x + 4 <
Answers
GPT-4o mini
To determine the correct model and inequality that represents the problem, let's analyze the situation.
Jared is building a square pen and using fencing wire for the perimeter. The perimeter \( P \) of a square pen is calculated using the formula:
\[ P = 4x \]
where \( x \) is the side length of the square. Jared has a total of 140 feet of fencing wire to use for the perimeter. Therefore, we want the perimeter \( P \) to be less than or equal to 140 feet (since he can choose to use less fencing wire if he wants).
This gives us the inequality:
\[ 4x \leq 140 \]
However, since none of the answer choices explicitly show \( 4x \leq 140 \), we can simplify it. The closest inequality that represents using all of the fencing or less is:
- If we want to say that he uses less than the full amount but can possibly use it all, we could use the inequality \( 4x < 140 \).
Thus, the answer that best represents Jared's situation (allowing for the possible use of all the fencing) is:
**Option A: 4x < 140**
Jared is building a square pen and using fencing wire for the perimeter. The perimeter \( P \) of a square pen is calculated using the formula:
\[ P = 4x \]
where \( x \) is the side length of the square. Jared has a total of 140 feet of fencing wire to use for the perimeter. Therefore, we want the perimeter \( P \) to be less than or equal to 140 feet (since he can choose to use less fencing wire if he wants).
This gives us the inequality:
\[ 4x \leq 140 \]
However, since none of the answer choices explicitly show \( 4x \leq 140 \), we can simplify it. The closest inequality that represents using all of the fencing or less is:
- If we want to say that he uses less than the full amount but can possibly use it all, we could use the inequality \( 4x < 140 \).
Thus, the answer that best represents Jared's situation (allowing for the possible use of all the fencing) is:
**Option A: 4x < 140**