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.

Question

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

A
.

21 ft3

B.

36 ft3

C.

28.5 ft3

D.

43.5 ft3

Answer 1

Let's break down the problem step by step.

1. Fertilizer Added After 5 Weeks:
   The farm deposits 1.5 ft³ of fertilizer each week. After 5 weeks, the amount of fertilizer added is: \[ 1.5 , \text{ft}^3/\text{week} \times 5 , \text{weeks} = 7.5 , \text{ft}^3 \] This means that after 5 weeks, the total amount of fertilizer in the container is: \[ 7.5 , \text{ft}^3 \]

2. Fertilizer Added in Additional 14 Weeks:
   After the initial 5 weeks, it takes another 14 weeks to fill the container. The amount of fertilizer added during these 14 weeks is: \[ 1.5 , \text{ft}^3/\text{week} \times 14 , \text{weeks} = 21 , \text{ft}^3 \]

3. Total Amount of Fertilizer in the Container:
   The total amount of fertilizer in the container after the additional 14 weeks would be: \[ 7.5 , \text{ft}^3 + 21 , \text{ft}^3 = 28.5 , \text{ft}^3 \]

Thus, the capacity of the storage container is 28.5 ft³.

The correct answer is C. 28.5 ft³.