Question 10

6 1/2 cups of flour will be needed to make 90 cookies.

To scale the recipe from 36 cookies to 90 cookies, the amount of flour required increases proportionally. The calculation shows that 2 1/2 cups of flour is needed for every 36 cookies, which results in needing 6 1/2 cups for 90 cookies.

A) 6 1/2 cups

This option is correct because to find the necessary amount of flour for 90 cookies, we first determine the ratio of cookies to flour. Since 36 cookies require 2 1/2 cups of flour, we can set up a proportion: (2 1/2 cups / 36 cookies) = (x cups / 90 cookies). Solving this gives x = 6 1/2 cups.

B) 10 1/2 cups

This option is incorrect as it overestimates the amount of flour needed. While calculating the scaling for 90 cookies, 10 1/2 cups exceeds the proportionate increase from 36 cookies and does not align with the original ratio provided in the recipe.

C) 5 1/2 cups

This option is also incorrect because it underestimates the amount of flour required. The calculation based on the recipe's original proportions indicates that less than this amount would not yield the necessary 90 cookies, making it insufficient.

D) 4 1/2 cups

This option is incorrect as it significantly underestimates the flour needed for 90 cookies. The original recipe's flour requirement must be scaled up, and 4 1/2 cups does not meet the necessary increase from 36 to 90 cookies, thus failing to provide the correct amount.

Conclusion

The correct answer, 6 1/2 cups, is derived from accurately scaling the flour amount based on the original recipe's proportions. All other options fail to reflect the proper ratio needed for the increased number of cookies, making them incorrect choices.