Final answer:
To find the total capacity of the bird feeder, set up a proportion where 3/4 of the total capacity equals 5 1/2 cups. Solve for the total capacity to get 7 1/3 cups, but since this is not an answer choice and options are whole numbers, the closest correct answer option, presumably rounding down, is 7 cups.
Step-by-step explanation:
The question asks how many total cups of birdseed a bird feeder will hold if it is 3/4 full after adding 5 1/2 cups of birdseed. To find the total capacity, we use the proportion that 3/4 of the total capacity is equal to 5 1/2 cups. We set up the following equation to solve for the total capacity (T):
(3/4) * T = 5 1/2 cups
We then convert 5 1/2 cups to an improper fraction which is 11/2 cups. Now, we have:
(3/4) * T = 11/2
Next, we solve for T by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3:
T = (11/2) * (4/3)
When we multiply these fractions, we get T = 22/3, which is equal to 7 1/3 cups. However, this is not an option among the provided answers. Since we must answer with one of the choices given, we might suspect a typo in the question or answer options. Based on the closest option, the correct answer would be B) 7 cups, assuming the options were supposed to be whole numbers.