To find the ratio at which the constant of proportionality appears, we need to look at how raspberry scoops relate to the cups of lemonade based on the given data.
The table shows the following relationships:
- For 1 scoop of raspberry, there are 2.5 cups of lemonade.
- For 2 scoops of raspberry, there are 5 cups of lemonade.
- For 4 scoops of raspberry, there are 10 cups of lemonade.
- For 6 scoops of raspberry, there are 15 cups of lemonade.
Let's find the constant of proportionality:
- Ratio of scoops of raspberry to cups of lemonade:
- For the pair (1, 2.5): The ratio is 1/2.5 = 0.4
- For the pair (2, 5): The ratio is 2/5 = 0.4
- For the pair (4, 10): The ratio is 4/10 = 0.4
- For the pair (6, 15): The ratio is 6/15 = 0.4
All these pairs maintain the same ratio, confirming that the relationship is proportional (the constant of proportionality is 0.4).
Next, to identify the response that matches the pairs from the options provided:
- (1, 2.5) corresponds to 1 scoop of raspberry for 2.5 cups of lemonade.
- (2, 5) corresponds to 2 scoops of raspberry for 5 cups of lemonade.
Both these pairs give the ratio needed for the constant of proportionality.
The correct option that directly corresponds to the ratio of scoops of raspberry to cups of lemonade is:
(2, 5).
So, Rosie should use the ratio represented as (2, 5) to maintain the constant of proportionality when making rasperry lemonade.
1 answer