A local farm deposits 1.5 ft3

of fertilizer into a storage container at a garden store each week. After 5 weeks, the container has 15 ft3
of fertilizer.

If it takes 14 more weeks for the storage container to be filled, what is the capacity of the storage container?

(1 point)
Responses

43.5 ft3
43.5 ft3

28.5 ft3
28.5 ft3

36 ft3
36 ft3

21 ft3

1 answer

To find the total capacity of the storage container, we start by determining how much fertilizer is deposited over the total period of time mentioned.

  1. The farm deposits 1.5 ft³ of fertilizer each week.
  2. After 5 weeks, they have deposited:

\[ 1.5 , \text{ft}^3/\text{week} \times 5 , \text{weeks} = 7.5 , \text{ft}^3 \]

This means that at the end of 5 weeks, there are already 7.5 ft³ in the container.

  1. It is stated that after 5 weeks, the total amount of fertilizer in the container is 15 ft³. This means an additional 7.5 ft³ of fertilizer must already be in the container when they started depositing (since \(15 , \text{ft}^3 - 7.5 , \text{ft}^3 = 7.5 , \text{ft}^3\)).

  2. After the initial 5 weeks, it takes 14 more weeks to fill the container. During these 14 weeks, the farm adds more fertilizer:

\[ 1.5 , \text{ft}^3/\text{week} \times 14 , \text{weeks} = 21 , \text{ft}^3 \]

  1. Adding this to the 15 ft³ already in the container gives:

\[ 15 , \text{ft}^3 + 21 , \text{ft}^3 = 36 , \text{ft}^3 \]

Thus, the total capacity of the storage container is:

\[ \boxed{36 , \text{ft}^3} \]