To solve this problem, let's determine the proportion of crocodiles to alligators in each lake and then compare these proportions to find out which two lakes have the same proportion.
Here is the data given in the table format:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Lake} & \text{Crocodiles} & \text{Alligators} \\
\hline
A & 4 & 5 \\
\hline
B & 21 & 35 \\
\hline
C & 3 & 9 \\
\hline
D & 6 & 16 \\
\hline
E & 24 & 30 \\
\hline
\end{array}
\][/tex]
First, we calculate the ratio of crocodiles to alligators in each lake:
1. Lake A:
[tex]\[
\text{Ratio} = \frac{4}{5} = 0.8
\][/tex]
2. Lake B:
[tex]\[
\text{Ratio} = \frac{21}{35} = \frac{3}{5} = 0.6
\][/tex]
3. Lake C:
[tex]\[
\text{Ratio} = \frac{3}{9} = \frac{1}{3} \approx 0.333
\][/tex]
4. Lake D:
[tex]\[
\text{Ratio} = \frac{6}{16} = \frac{3}{8} = 0.375
\][/tex]
5. Lake E:
[tex]\[
\text{Ratio} = \frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
Now, we compare the ratios to identify which two lakes have the same proportion:
- Lake A and Lake B:
[tex]\[
0.8 \neq 0.6
\][/tex]
- Lake B and Lake C:
[tex]\[
0.6 \neq 0.333
\][/tex]
- Lake C and Lake D:
[tex]\[
0.333 \neq 0.375
\][/tex]
- Lake A and Lake E:
[tex]\[
0.8 = 0.8
\][/tex]
- Lake B and Lake D:
[tex]\[
0.6 \neq 0.375
\][/tex]
From the comparison, we see that Lake A and Lake E have the same proportion of crocodiles to alligators, which is [tex]\(\frac{4}{5}\)[/tex] or 0.8.
Therefore, the correct answer is:
C. Lake A and Lake E
