Answered

Rachel traveled to five different areas (A, B, C, D, and E) to study the number of buckeye butterflies and the number of monarch butterflies living there. The table shows her findings.

\begin{tabular}{|l|r|r|}
\hline
Area & Buckeye Butterflies & Monarch Butterflies \\
\hline
A & 15 & 16 \\
\hline
B & 27 & 36 \\
\hline
C & 12 & 25 \\
\hline
D & 24 & 32 \\
\hline
E & 44 & 33 \\
\hline
\end{tabular}

The relationship between the number of buckeye butterflies and the number of monarch butterflies is not proportional across all areas. Which two areas have buckeyes and monarchs in the same proportion?

A. areas A and B
B. areas C and E
C. areas B and D
D. areas C and D



Answer :

GinnyAnswer
To determine which two areas have buckeye and monarch butterflies in the same proportion, we need to calculate the ratio of buckeye butterflies to monarch butterflies for each area. Let's start by calculating these ratios:

1. Area A:
- Buckeye Butterflies: 15
- Monarch Butterflies: 16
- Ratio: [tex]\( \frac{15}{16} = 0.9375 \)[/tex]

2. Area B:
- Buckeye Butterflies: 27
- Monarch Butterflies: 36
- Ratio: [tex]\( \frac{27}{36} = 0.75 \)[/tex]

3. Area C:
- Buckeye Butterflies: 12
- Monarch Butterflies: 25
- Ratio: [tex]\( \frac{12}{25} = 0.48 \)[/tex]

4. Area D:
- Buckeye Butterflies: 24
- Monarch Butterflies: 32
- Ratio: [tex]\( \frac{24}{32} = 0.75 \)[/tex]

5. Area E:
- Buckeye Butterflies: 44
- Monarch Butterflies: 33
- Ratio: [tex]\( \frac{44}{33} \approx 1.3333 \)[/tex]

Now, we compare the ratios to find which areas have the same proportion of buckeye to monarch butterflies:

- Area A: 0.9375
- Area B: 0.75
- Area C: 0.48
- Area D: 0.75
- Area E: 1.3333

We observe that Area B and Area D both have a ratio of 0.75. Therefore, the two areas that have buckeye and monarch butterflies in the same proportion are Area B and Area D.

Hence, the correct answer is:
C. areas B and D