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.
| Area | Buckeye Butterflies | Monarch Butterflies |
|---|---|---|
| A | 15 | 16 |
| B | 27 | 36 |
| C | 12 | 25 |
| D | 24 | 32 |
| E | 44 | 33 |
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 [tex]$A$[/tex] and [tex]$B$[/tex]
B. areas [tex]$C$[/tex] and [tex]$E$[/tex]
C. areas [tex]$B$[/tex] and [tex]$D$[/tex]
D. areas [tex]$C$[/tex] and [tex]$D$[/tex]
Answer (2)
The ratios of buckeye butterflies to monarch butterflies were calculated for five areas. Areas B and D both have the same ratio of 0.75. Therefore, the answer is C. areas B and D.
;
Calculate the ratio of Buckeye to Monarch butterflies for each area.
Simplify the ratios for each area.
Compare the simplified ratios to identify matching proportions.
Areas B and D have the same ratio: 4 3 . Therefore, the answer is C .
Explanation
Analyzing the Ratios Let's analyze the ratios of Buckeye butterflies to Monarch butterflies in each area to determine which two areas have the same proportion.
Ratio for Area A Area A: The ratio is 16 15 = 0.9375 .
Ratio for Area B Area B: The ratio is 36 27 = 4 3 = 0.75 .
Ratio for Area C Area C: The ratio is 25 12 = 0.48 .
Ratio for Area D Area D: The ratio is 32 24 = 4 3 = 0.75 .
Ratio for Area E Area E: The ratio is 33 44 = 3 4 = 1.333... .
Comparing Ratios Comparing the ratios, we see that Area B and Area D both have a ratio of 0.75.
Conclusion Therefore, areas B and D have buckeyes and monarchs in the same proportion.
Examples
Understanding proportions is useful in many real-life situations. For example, if you're mixing a cleaning solution, you need to maintain the correct ratio of cleaner to water to ensure it's effective but not too strong. Similarly, in cooking, maintaining the right proportions of ingredients is crucial for the recipe to turn out as expected. In finance, understanding ratios helps in analyzing a company's financial health by comparing its assets to its liabilities.
