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Part 1
You are making a new recipe for dinner. The recipe has the following proportional relationship.
12 cups of cat for 4 cups of sauce
48 cups of cat for 16 cups of sauce
Find the constant of proportionality. Find how many cups of cat you need for 8 cups of sauce.
To find the constant of proportionality, we can divide the number of cups of cat by the number of cups of sauce in each scenario.
For the first scenario, we have 12 cups of cat for 4 cups of sauce. So the constant of proportionality is 12/4 = 3 cups of cat per cup of sauce.
For the second scenario, we have 48 cups of cat for 16 cups of sauce. Again, the constant of proportionality is 48/16 = 3 cups of cat per cup of sauce.
So, the constant of proportionality is 3 cups of cat per cup of sauce.
To find how many cups of cat are needed for 8 cups of sauce, we multiply the number of cups of sauce by the constant of proportionality.
8 cups of sauce multiplied by 3 cups of cat per cup of sauce equals 24 cups of cat.
Therefore, you would need 24 cups of cat for 8 cups of sauce in this recipe.