To determine which two lakes have crocodiles and alligators in the same proportion, we need to calculate the ratio of crocodiles to alligators for each lake and then compare these ratios.
Here is the data from the table:
[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, let’s calculate the ratios:
- For Lake [tex]\( A \)[/tex]:
[tex]\[
\frac{\text{Crocodiles}}{\text{Alligators}} = \frac{4}{5} = 0.8
\][/tex]
- For Lake [tex]\( B \)[/tex]:
[tex]\[
\frac{\text{Crocodiles}}{\text{Alligators}} = \frac{21}{35} = \frac{3}{5} = 0.6
\][/tex]
- For Lake [tex]\( C \)[/tex]:
[tex]\[
\frac{\text{Crocodiles}}{\text{Alligators}} = \frac{3}{9} = \frac{1}{3} \approx 0.33
\][/tex]
- For Lake [tex]\( D \)[/tex]:
[tex]\[
\frac{\text{Crocodiles}}{\text{Alligators}} = \frac{6}{16} = \frac{3}{8} = 0.375
\][/tex]
- For Lake [tex]\( E \)[/tex]:
[tex]\[
\frac{\text{Crocodiles}}{\text{Alligators}} = \frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
Now, we compare the ratios:
- Lake [tex]\( A \)[/tex] has a ratio of 0.8.
- Lake [tex]\( B \)[/tex] has a ratio of 0.6.
- Lake [tex]\( C \)[/tex] has a ratio of 0.33.
- Lake [tex]\( D \)[/tex] has a ratio of 0.375.
- Lake [tex]\( E \)[/tex] has a ratio of 0.8.
We observe that Lake [tex]\( A \)[/tex] and Lake [tex]\( E \)[/tex] both have the same ratio of 0.8.
Therefore, the correct answer is:
C. Lake [tex]$A$[/tex] and Lake [tex]$E$[/tex]
