Use the table to answer the question.
Raspberry / Lemonade
1 | 2.5
2 | 5
4 | 10
6 | 15
Rosie is planning to make raspberry lemonade for a party she needs to add 2 scoops of raspberry to every 5 cups of lemonade the data table shows the ratios needed at what ratio does the constant of proportionality appear?
1. (1, 2.5)
2. (2.5, 1)
3. (2, 5)
4. (5, 2)
The constant of proportionality appears at the ratio (2, 5).
Explanation:
From the table, we can see the following ratios between the number of scoops of raspberry and the number of cups of lemonade:
- When there is 1 scoop of raspberry, there are 2.5 cups of lemonade. This can be written as 1:2.5.
- When there are 2 scoops of raspberry, there are 5 cups of lemonade. This can be written as 2:5.
- When there are 4 scoops of raspberry, there are 10 cups of lemonade. This can be written as 4:10.
- When there are 6 scoops of raspberry, there are 15 cups of lemonade. This can be written as 6:15.
We can see that the ratio of the number of scoops of raspberry to the number of cups of lemonade remains constant at 2:5.
The constant of proportionality appears in the ratio (2, 5).
To find the ratio at which the constant of proportionality appears, we need to look for a consistent relationship between the number of scoops of raspberry and the number of cups of lemonade.
Looking at the table, we can see that as the number of scoops of raspberry doubles, the number of cups of lemonade also doubles. For example, when there are 2 scoops of raspberry, there are 5 cups of lemonade, and when there are 4 scoops of raspberry, there are 10 cups of lemonade.
Therefore, we can conclude that the constant of proportionality appears at a ratio of (2, 5).