Final answer:
Rob will need 22.67 cups of butter to make 34 dozen donuts. Therefore, he will not have enough butter left over to have any cups left.
Step-by-step explanation:
To find the answer, we first need to determine how many cups of butter are used for each dozen donuts.
The recipe calls for 1/2 pound of butter per 1.5 dozen donuts.
Since 1 pound of butter is equal to 2 cups, 1/2 pound of butter is equal to 1 cup.
Therefore, for each 1.5 dozen donuts, 1 cup of butter is used.
Next, we need to calculate how many cups of butter are needed to make 34 dozen donuts. Since 1 cup of butter is used for each 1.5 dozen donuts, we can set up a proportion:
1 cup / 1.5 dozen = x cups / 34 dozen
Cross-multiplying, we get:
x = (1 cup * 34 dozen) / 1.5 dozen
Simplifying, we get:
x = 34/1.5
x = 22.67 cups
Therefore, Rob will need 22.67 cups of butter to make 34 dozen donuts.
Subtracting this amount from the initial 9 pounds of butter, we can calculate the remaining amount of butter:
9 pounds * 2 cups/pound - 22.67 cups = 18 cups - 22.67 cups
= -4.67 cups
Since the value is negative, it means that Rob will not have enough butter to make 34 dozen donuts.
Therefore, the answer is none of the given choices (a. 4 cups, b. 6 cups, c. 8 cups, d. 10 cups).