To find the constant of proportionality, we can look at the ratio of raspberry to lemonade in the recipe for raspberry lemonade that Rosie is using.
According to the recipe, for every 2 scoops of raspberry, Rosie needs 5 cups of lemonade. This gives us a ratio of raspberry to lemonade as:
\[ \text{Ratio} = \frac{\text{scoops of raspberry}}{\text{cups of lemonade}} = \frac{2}{5} \]
The constant of proportionality is found by dividing the two quantities. In this case, it is:
\[ \text{Constant of Proportionality} = \frac{2}{5} = 0.4 \]
Now, we can match this with the proposed options. The ratio of raspberry to lemonade is given by (raspberry, lemonade):
- (2.5, 1) → This is not aligned with our calculation.
- (2, 5) → This also does not represent the right ratio.
- (1, 2.5) → This is not correct; it is the reciprocal.
- (5, 2) → Although it's also not correct for our ratio, it is the reciprocal.
Given these options, the one that most closely reflects the proper relationship (assuming we could ordain both ways) would be:
(2, 5) representing the proper use in the context.
However, you wanted the specific constant of proportionality based ratio which is:
\((1, 2.5)\)
Representing it in the context of lemonade to raspberry by reciprocal. Hence:
(1, 2.5) is the correct answer for what would give the proportion representing lemonade cups against scoops in our context.
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