Rebekah's recipe for 4 1/2 dozen cookies calls for 6 cups of sugar. How many cups of sugar are needed to make 8 dozen cookies?
Is the correct answer 10 2/3 cups?
(8/4.5)* 6 = 10.667.
yes. That is 10 2/3 cups sugar
To find out how many cups of sugar are needed to make 8 dozen cookies, we can use a proportion.
Let's set up our proportion by comparing the number of cookies to the amount of sugar:
(Number of cookies / Amount of sugar) = (Number of cookies / Amount of sugar)
We are given that Rebekah's recipe for 4 1/2 dozen cookies uses 6 cups of sugar. So we can substitute the values into the equation:
(4 1/2 dozen / 6 cups) = (8 dozen / x cups)
To solve for x (the amount of sugar needed for 8 dozen cookies), we can cross-multiply:
(4 1/2 dozen) * (x cups) = (8 dozen) * (6 cups)
Now let's convert the mixed number 4 1/2 into an improper fraction:
4 1/2 = (9/2)
Substituting the values:
(9/2 * x) = (8 dozen) * (6 cups)
To simplify, we can multiply 8 dozen by 6 cups:
(9/2 * x) = (8 * 6) cups
Now we can solve for x by dividing both sides of the equation by 9/2:
x = (8 * 6) cups / (9/2)
Simplifying further, let's multiply:
x = 48 cups / (9/2)
To divide by a fraction, we can multiply by its reciprocal:
x = 48 cups * (2/9)
Multiplying further, we get:
x = (48 * 2) cups / 9
x = 96 cups / 9
Now, divide 96 cups by 9:
x = 10 2/3 cups
So, the correct answer is indeed 10 2/3 cups of sugar.