A recipe for cookies calls for 7 1/2 cups of flour. If the recipe is for 2 dozen​ cookies, how much flour is needed for 13 dozen​ cookies?

7.5/ 24 = x/156

Cross multiply and solve for x.

You want 13/2 as many cookies, so use 13/2 as much flour:

(13/2) * (7 1/2) = 48 3/4 cups

To find out how much flour is needed for 13 dozen​ cookies, let's first calculate how much flour is needed for 1 dozen​ cookies.

1 dozen​ cookies = 12 cookies

The recipe calls for 7 1/2 cups of flour for 2 dozen​ cookies.

Flour needed for 1 dozen​ cookies = (7 1/2 cups of flour) / (2 dozen​ cookies) = (15/2) cups of flour

Now, let's calculate how much flour is needed for 13 dozen​ cookies.

Flour needed for 13 dozen​ cookies = (Flour needed for 1 dozen​ cookies) * (13 dozen​ cookies)
= (15/2) cups of flour * 13 dozen​ cookies

To simplify the calculation, let's express 13 dozen​ cookies as 156 cookies.

Flour needed for 13 dozen​ cookies = (15/2) cups of flour * 156 cookies
= (15/2) * 156/1 cups of flour
= 15 * 156 / 2 cups of flour
= 2340 / 2 cups of flour
= 1170 cups of flour

Therefore, 1170 cups of flour are needed for 13 dozen​ cookies.

To determine how much flour is needed for 13 dozen cookies, you need to calculate the ratio between the number of cookies in the original recipe and the desired number of cookies.

The original recipe is for 2 dozen cookies, which is equal to 2 × 12 = 24 cookies.

Now, let's find the ratio of cookies:

Number of cookies in the original recipe = 24
Number of cookies desired = 13 × 12 = 156

Ratio = Number of cookies desired / Number of cookies in the original recipe = 156 / 24 = 6.5

Next, you need to determine how much flour is needed for 6.5 times the original recipe.

Amount of flour needed for the original recipe = 7 1/2 cups

Amount of flour needed for 6.5 times the original recipe = (7 1/2) × 6.5

To calculate this, you can convert 7 1/2 to an improper fraction: 7 1/2 = 15/2

Amount of flour needed for 6.5 times the original recipe = (15/2) × 6.5

Multiply the numerators and the denominators:

Amount of flour needed = 15 × 6.5 / 2 = 97.5 / 2 = 48.75 cups

Therefore, you would need 48.75 cups of flour for 13 dozen cookies.