Raspberry: 1, 2, 4, 6
Lemonade: 2.5, 5, 10, 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 ratio needed. At what ratio does the constant of proportionality appear?
Options:
(5, 2)
(2, 5)
(1, 2.5)
(2.5, 1)
The ratio at which the constant of proportionality appears can be found by comparing the number of scoops of raspberry to the number of cups of lemonade. Looking at the data table, we can see that for every 2 scoops of raspberry, there are 5 cups of lemonade.
Therefore, the ratio at which the constant of proportionality appears is (2, 5).
To find the ratio at which the constant of proportionality appears, we need to compare the number of cups of lemonade to the number of scoops of raspberry needed.
Looking at the data provided:
- For Raspberry: 1 scoop is needed for 2 cups, 2 scoops for 4 cups, and 3 scoops for 6 cups.
- For Lemonade: 2.5 cups are needed for 5 scoops, 5 cups for 10 scoops, and 7.5 cups for 15 scoops.
Comparing the ratios, we have:
(2, 5): 2 cups of lemonade requires 5 scoops of raspberry (not a constant ratio).
(5, 2): 5 cups of lemonade requires 2 scoops of raspberry (not a constant ratio).
(1, 2.5): 1 cup of lemonade requires 2.5 scoops of raspberry (not a constant ratio).
(2.5, 1): 2.5 cups of lemonade require 1 scoop of raspberry.
Therefore, the ratio at which the constant of proportionality appears is (2.5, 1).
To find the ratio at which the constant of proportionality appears, we can compare the quantities of raspberries and lemonade in each pair.
Looking at the given data table:
Raspberry: 1, 2, 4, 6
Lemonade: 2.5, 5, 10, 15
Let's create a ratio for each pair, by dividing the quantity of raspberries by the quantity of lemonade:
Ratio for the first pair: 1/2.5 = 0.4
Ratio for the second pair: 2/5 = 0.4
Ratio for the third pair: 4/10 = 0.4
Ratio for the fourth pair: 6/15 = 0.4
We can see that the ratio is the same for all the pairs, which means the constant of proportionality appears at the ratio (0.4).
However, none of the given options match this ratio. The closest option is (1, 2.5), but it is not an exact match.