Question
Multiple Choice Question 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? A. 21 ft3 B. 36 ft3 C. 28.5 ft3 D. 43.5 ft3
Answers
GPT-4o mini
To determine the capacity of the storage container, we first need to calculate how much fertilizer is deposited into the container over the total time period.
We know that:
- The farm deposits 1.5 ft³ of fertilizer each week.
- After 5 weeks, the container already has 15 ft³ of fertilizer.
Next, we can calculate the amount of fertilizer deposited over the initial 5 weeks:
\[
\text{Fertilizer after 5 weeks} = 1.5 \, \text{ft}^3/\text{week} \times 5 \, \text{weeks} = 7.5 \, \text{ft}^3
\]
Now, we add this to the amount already stated in the problem (15 ft³). This means that 15 ft³ likely includes the total amount deposited after 5 weeks, so there appears to be a miscommunication in the accumulated amount.
Next, we check if the "string" follows correctly with the additional 14 weeks of deposits.
In the total of 14 more weeks:
\[
\text{Fertilizer for 14 weeks} = 1.5 \, \text{ft}^3/\text{week} \times 14 \, \text{weeks} = 21 \, \text{ft}^3
\]
Now, we add this to the 15 ft³ that was already in the container after the first 5 weeks:
\[
\text{Total capacity} = 15 \, \text{ft}^3 + 21 \, \text{ft}^3 = 36 \, \text{ft}^3
\]
Thus, the capacity of the storage container is:
\[
\boxed{36 \, \text{ft}^3}
\]
So, the answer is B. 36 ft³.
We know that:
- The farm deposits 1.5 ft³ of fertilizer each week.
- After 5 weeks, the container already has 15 ft³ of fertilizer.
Next, we can calculate the amount of fertilizer deposited over the initial 5 weeks:
\[
\text{Fertilizer after 5 weeks} = 1.5 \, \text{ft}^3/\text{week} \times 5 \, \text{weeks} = 7.5 \, \text{ft}^3
\]
Now, we add this to the amount already stated in the problem (15 ft³). This means that 15 ft³ likely includes the total amount deposited after 5 weeks, so there appears to be a miscommunication in the accumulated amount.
Next, we check if the "string" follows correctly with the additional 14 weeks of deposits.
In the total of 14 more weeks:
\[
\text{Fertilizer for 14 weeks} = 1.5 \, \text{ft}^3/\text{week} \times 14 \, \text{weeks} = 21 \, \text{ft}^3
\]
Now, we add this to the 15 ft³ that was already in the container after the first 5 weeks:
\[
\text{Total capacity} = 15 \, \text{ft}^3 + 21 \, \text{ft}^3 = 36 \, \text{ft}^3
\]
Thus, the capacity of the storage container is:
\[
\boxed{36 \, \text{ft}^3}
\]
So, the answer is B. 36 ft³.