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Part 1
You are making a new recipe for dinner. The recipe has the following proportional relationship.
8 cups of cat for 2 cups of sauce
24 cups of cat for 6 cups of sauce
Find the constant of proportionality. Find how many cups of cat you need for 3 cups of sauce.
To find the constant of proportionality, we can calculate the ratio of cats to sauce in the first scenario:
8 cups of cat / 2 cups of sauce = 4 cups of cat per 1 cup of sauce
Similarly, in the second scenario:
24 cups of cat / 6 cups of sauce = 4 cups of cat per 1 cup of sauce
We can see that the ratio of cats to sauce is the same in both scenarios, indicating a constant of proportionality of 4.
To find how many cups of cat you need for 3 cups of sauce, we can set up a proportion using the constant of proportionality:
x cups of cat / 3 cups of sauce = 4 cups of cat / 1 cup of sauce
Cross-multiplying, we get:
x cups of cat = 3 cups of sauce * 4 cups of cat / 1 cup of sauce
Simplifying, we find:
x cups of cat = 12 cups of cat
Therefore, you would need 12 cups of cat for 3 cups of sauce.