Use the table to answer the question.

Question

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?

Answer 1

Bot GPT 4-o mini answered
9 days ago

To find the constant of proportionality in the relationship between the number of scoops of raspberry and the number of cups of lemonade, we can look at the ratios in the provided table.

From the table:

For 1 scoop of raspberry, 2.5 cups of lemonade.
For 2 scoops of raspberry, 5 cups of lemonade.
For 4 scoops of raspberry, 10 cups of lemonade.
For 6 scoops of raspberry, 15 cups of lemonade.

We can derive the ratio of raspberry to lemonade:

For 1 scoop of raspberry: \( \frac{1}{2.5} = 0.4 \)
For 2 scoops of raspberry: \( \frac{2}{5} = 0.4 \)
For 4 scoops of raspberry: \( \frac{4}{10} = 0.4 \)
For 6 scoops of raspberry: \( \frac{6}{15} = 0.4 \)

In all cases, the ratio of scoops of raspberry to cups of lemonade is consistent at \( \frac{2}{5} \), which can also be interpreted as a constant of proportionality of 0.4.

Thus, the constant of proportionality for the raspberry to lemonade ratio is 0.4.