Question

A local farm deposits 1.5 ft^3 of fertilizer into a storage container at a garden store each week. After 5 weeks the container has 15 ft^3 of fertilizer.

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

A.
21 ft^3

B.
36 ft^3

C.
28.5 ft^3

D.
43.5 ft^3

Answer 1

First, let's find out how much fertilizer is added to the storage container over the total time period.

The farm deposits 1.5 ft³ of fertilizer each week. After 5 weeks, the amount of fertilizer added is:

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

So, after 5 weeks, the total amount of fertilizer in the container is:

\[
7.5 \, \text{ft}^3
\]

However, the problem states that there is already 15 ft³ of fertilizer in the container after 5 weeks. This indicates that there was already some fertilizer in the container before the 5 weeks started.

Next, let's determine how much more fertilizer is added in the next 14 weeks. In 14 weeks, the additional amount of fertilizer added will be:

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

Now, we can calculate the total amount of fertilizer after the full 19 weeks (5 weeks + 14 weeks):

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

Thus, the capacity of the storage container is:

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