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?
The constant of proportionality appears at the ratio of 2 scoops of raspberry to 5 cups of lemonade.
To find the ratio at which the constant of proportionality appears, we need to identify a consistent relationship between the two quantities: the number of scoops of raspberry and the cups of lemonade.
Looking at the data provided:
Raspberry Lemonade
1 2.5
2 5
4 10
6 15
We can observe that as the number of scoops of raspberry doubles, the cups of lemonade needed also doubles. This consistent relationship indicates that the ratio between the number of scoops of raspberry and the cups of lemonade is constant.
Let's calculate the ratio for each case by dividing the number of scoops of raspberry by the cups of lemonade:
1/2.5 ≈ 0.4
2/5 = 0.4
4/10 = 0.4
6/15 = 0.4
As we can see, the ratio between scoops of raspberry and cups of lemonade is consistently 0.4 in each case. Therefore, the constant of proportionality appears at a ratio of 0.4.
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.
By observing the data table, we can see that for every 2 scoops of raspberry, there are 5 cups of lemonade. Let's simplify this ratio:
2 scoops of raspberry : 5 cups of lemonade
To simplify the ratio, we can divide both sides by the greatest common divisor (GCD) of the two numbers. In this case, the GCD of 2 and 5 is 1:
2/1 : 5/1
The simplified ratio is:
2 : 5
Therefore, the constant of proportionality appears at a ratio of 2 : 5.