Raspberry Lemonade

Question

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 point)
Responses

(1, 2.5)
left parenthesis 1 comma 2.5 right parenthesis

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(2.5, 1)
left parenthesis 2.5 comma 1 right parenthesis

(2, 5)

Answer 1

To find the constant of proportionality from the data given in the table, we need to analyze the relationship between the amount of raspberry and lemonade. The data in the table shows pairs of values for raspberry (x) and lemonade (y):

• (1, 2.5)
• (2, 5)
• (4, 10)
• (6, 15)

The ratio of raspberry to lemonade can be determined by looking for the constant relationship. The ratio for each pair can be calculated as follows:

1. For (1, 2.5): \(\frac{1}{2.5} = 0.4\)
2. For (2, 5): \(\frac{2}{5} = 0.4\)
3. For (4, 10): \(\frac{4}{10} = 0.4\)
4. For (6, 15): \(\frac{6}{15} = 0.4\)

The constant of proportionality is the same across all these pairs, which is \(0.4\).

Now considering the responses given, we need to reformat to reflect the proportion correctly. If we use the base ratio of raspberry to lemonade that gives us:

• For lemonade at 5 cups, the raspberry required is 2 scoops: so the ratio is \((2, 5)\).

Thus, the correct answer from the provided options that represents this ratio is:

(2, 5)