A chocolate chip recipe calls for 3 1/2 cups of flour to make 5 dozen cookies. How much flour is needed to make 3 dozen cookies?
If 3½ cups of flour make 5 dozen cookies, then 3½ / 5 = 7/10 cups of flour will make 1 dozen cookies.
Therefore, 7/10 * 3 = 21/10 = 2 1/10 cups of flour will make 3 dozen cookies.
since the flour/cookies ratio is constant,
x/3 = (3 1/2)/5
To find out how much flour is needed to make 3 dozen cookies, we can set up a proportion using the number of cookies and the amount of flour.
Let's call the unknown amount of flour needed to make 3 dozen cookies "x".
The proportion can be set up as:
5 dozen cookies / 3 1/2 cups of flour = 3 dozen cookies / x cups of flour
To solve for "x", we can cross multiply:
(5 dozen cookies) * (x cups of flour) = (3 1/2 cups of flour) * (3 dozen cookies)
5x = (7/2) * 3
5x = 21/2
To isolate "x", we can divide both sides by 5:
x = (21/2) / 5
x = 21/10 or 2 1/10 cups of flour
Therefore, to make 3 dozen cookies, you will need 2 1/10 cups of flour.
To find out how much flour is needed to make 3 dozen cookies instead of 5 dozen, we can set up a proportion.
First, let's determine the ratio of flour to cookies in the original recipe:
Original recipe: 3 1/2 cups of flour for 5 dozen cookies
To convert cups of flour to dozen cookies, we need to find the ratio of cups of flour to one dozen cookies.
To convert from cups to dozens, we divide the number of cups by 3 1/2 and divide the number of cookies by 5.
Let x represent the number of cups of flour needed for 3 dozen cookies.
Now we can set up the proportion:
3 1/2 cups of flour / 5 dozen cookies = x cups of flour / 3 dozen cookies
To solve for x, we need to cross-multiply:
(3 1/2) * 3 dozen cookies = 5 dozen cookies * x cups of flour
Simplifying the equation:
(7/2) * 3 dozen cookies = 5 dozen cookies * x cups of flour
21/2 dozen cookies = 5 dozen cookies * x cups of flour
Dividing both sides by 5 dozen cookies:
(21/2 dozen cookies) / (5 dozen cookies) = x cups of flour
21/2 / 5 = x cups of flour
Now we can simplify and solve for x:
21/2 divided by 5 equals 21/10
x = 21/10
Therefore, you would need 21/10 cups of flour to make 3 dozen cookies.