Rebekah's recipe for 41/2 dozen cookies call for 6 cups of sugar. How many cups of sugar are needed to make 8 dozen cookies?
4.5/6 = 8/x
Cross multiply and solve for x.
4.5x = 48
x = 10 2/3 cup
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To find out how many cups of sugar are needed to make 8 dozen cookies, we can use a proportion.
First, let's establish the relationship between the number of dozens of cookies and the cups of sugar. In Rebekah's recipe, 4 1/2 dozen cookies require 6 cups of sugar.
So, we can set up the proportion:
(4 1/2 dozen cookies) / (6 cups of sugar) = (8 dozen cookies) / (x cups of sugar)
To solve for x, we can cross-multiply and then solve for x:
(4 1/2) * x = 6 * 8
To simplify the left side, convert 4 1/2 to an improper fraction: 4 1/2 = (9/2).
Now we have:
(9/2) * x = 6 * 8
Multiply both sides of the equation:
9x/2 = 48
Next, to isolate x, we can multiply both sides of the equation by 2/9:
x = (2/9) * 48
Finally, compute the value of x:
x = 96/9
Divide to simplify:
x ≈ 10.67
Therefore, you would need approximately 10.67 cups of sugar to make 8 dozen cookies according to Rebekah's recipe.