Explain how to find the constant of proportionality for the ratio of robins to cardinals.
A 2-column table with 4 rows:
Column 1 labeled Cardinals with entries 5, 6, 9, 10.
Column 2 labeled Robins with entries 15, 18, 27, 30.
Answer (2)
The constant of proportionality for the ratio of robins to cardinals is 3. This means that for every cardinal, there are 3 robins. You find this constant by calculating the ratio of the number of robins to the number of cardinals for each pair of values and observing that they are all consistent.
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To find the constant of proportionality for the ratio of robins to cardinals, follow these steps:
Understand the Concept : The constant of proportionality is the number that you multiply by to go from one quantity to another when two quantities are directly proportional. In this context, it is the number that, when multiplied by the number of cardinals, gives you the number of robins.
Analyze the Given Table : You have a table with two columns representing cardinals and robins. The entries for cardinals are: 5, 6, 9, and 10. The corresponding entries for robins are: 15, 18, 27, and 30.
Calculate the Ratio for Each Row : Divide the number of robins by the number of cardinals for each pair.
For 5 cardinals and 15 robins : 5 15 = 3
For 6 cardinals and 18 robins : 6 18 = 3
For 9 cardinals and 27 robins : 9 27 = 3
For 10 cardinals and 30 robins : 10 30 = 3
Identify the Constant of Proportionality : Notice that in each case, the ratio of robins to cardinals is consistently equal to 3. This means the constant of proportionality is 3.
Conclusion : The constant of proportionality is 3, which indicates that for every cardinal, there are 3 robins. This consistent ratio shows how these quantities are proportionally related.
