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The dimensions and number of animals are given for different corrals.

\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{Corral} & \multicolumn{1}{|c|}{Length} & Width & Number of Animals \\
\hline
1 & 50 meters & 40 meters & 110 \\
\hline
2 & 60 meters & 35 meters & 115 \\
\hline
3 & 55 meters & 45 meters & 125 \\
\hline
4 & 65 meters & 40 meters & 130 \\
\hline
\end{tabular}

The population constraints state that each corral should have at least 20 square meters for each animal. Which corral meets this requirement?

A. Corral 1
B. Corral 2
C. Corral 3
D. Corral 4



Answer :

GinnyAnswer
To determine which corral meets the requirement of providing at least 20 square meters per animal, we follow these steps:

1. Calculate the area of each corral:
- Corral 1:
[tex]\( \text{Length} = 50 \, \text{meters}, \text{Width} = 40 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 50 \times 40 = 2000 \, \text{square meters} \][/tex]
- Corral 2:
[tex]\( \text{Length} = 60 \, \text{meters}, \text{Width} = 35 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 60 \times 35 = 2100 \, \text{square meters} \][/tex]
- Corral 3:
[tex]\( \text{Length} = 55 \, \text{meters}, \text{Width} = 45 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 55 \times 45 = 2475 \, \text{square meters} \][/tex]
- Corral 4:
[tex]\( \text{Length} = 65 \, \text{meters}, \text{Width} = 40 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 65 \times 40 = 2600 \, \text{square meters} \][/tex]

2. Calculate the required area for the animals in each corral:
- For each animal, 20 square meters are required. Thus, compute the required area based on the number of animals.
- Corral 1:
[tex]\( 110 \, \text{animals} \times 20 \, \text{square meters per animal} = 2200 \, \text{square meters} \)[/tex]
- Corral 2:
[tex]\( 115 \, \text{animals} \times 20 \, \text{square meters per animal} = 2300 \, \text{square meters} \)[/tex]
- Corral 3:
[tex]\( 125 \, \text{animals} \times 20 \, \text{square meters per animal} = 2500 \, \text{square meters} \)[/tex]
- Corral 4:
[tex]\( 130 \, \text{animals} \times 20 \, \text{square meters per animal} = 2600 \, \text{square meters} \)[/tex]

3. Compare the actual corral area with the required area:
- Corral 1: [tex]\( \text{Actual Area} = 2000 \, \text{square meters}, \text{Required Area} = 2200 \, \text{square meters} \)[/tex]
- [tex]\( 2000 < 2200 \)[/tex] (Does not meet the requirement)
- Corral 2: [tex]\( \text{Actual Area} = 2100 \, \text{square meters}, \text{Required Area} = 2300 \, \text{square meters} \)[/tex]
- [tex]\( 2100 < 2300 \)[/tex] (Does not meet the requirement)
- Corral 3: [tex]\( \text{Actual Area} = 2475 \, \text{square meters}, \text{Required Area} = 2500 \, \text{square meters} \)[/tex]
- [tex]\( 2475 < 2500 \)[/tex] (Does not meet the requirement)
- Corral 4: [tex]\( \text{Actual Area} = 2600 \, \text{square meters}, \text{Required Area} = 2600 \, \text{square meters} \)[/tex]
- [tex]\( 2600 \geq 2600 \)[/tex] (Meets the requirement)

4. Conclusion:
The only corral that meets the requirement of providing at least 20 square meters per animal is Corral 4.

Answer: D. Corral 4

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