Answer:
They can make 4 whole batches of a dozen cookies
Explanation:
From the question, we have;
The quantity of flour they need to make a dozen cookie = 3/4 cup
The amount of butter they need to make a dozen cookie = 1/3 cup
The quantity of flour Ruby brought = 2 cups
The amount of butter Ruby brought = 1/4 cups
The quantity of flour Joey brought = 1 cups
The amount of butter Joey brought = 1/2 cups
The quantity of flour Sully brought = 1 1/4 cups
The amount of butter Sully brought = 3/4 cups
The total quantity of flour they have, W = 2 + 1 + 1 1/4 = 17/4 = 4.25
∴ The total quantity of flour they have, W = 4.25 cups
The total amount of butter that they have, B = 1/4 + 1/2 + 3/4 = 3/2
∴ The total amount of butter that they have, B = 3/2 cups
The ratio of the quantity of flour to the amount of butter for making a cake is given as follows;
Flour to butter ratio = 3/4 cup/(1/3 cup) = 9/4 = 9:4
The flour to butter ratio that they have = 4.25/(3/2) = 17/6 = (9 + 8)/(4 + 2)
Therefore, they have an excess amount of flour
The amount of flour they need, m = (9/4) × (3/2) cups = 3.375 cups of flour
3/4 cups of flour will make 1 dozen cookies
∴ 3.375 cups of flour will make (1/(3/4)×3.375 = 4.5 dozen cookies
Therefore;
The number of whole batches of a dozen cookies they can make = 4 whole batches of a dozen cookies