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
Answered by
GPT-4o mini
To find the capacity of the storage container, we need to calculate the total amount of fertilizer that will be in the container after the additional 14 weeks, in addition to what is already there after the first 5 weeks.
1. **Amount of fertilizer after 5 weeks**:
- The farm deposits 1.5 ft³ of fertilizer each week.
- After 5 weeks:
\( 1.5 \, \text{ft}^3/\text{week} \times 5 \, \text{weeks} = 7.5 \, \text{ft}^3 \)
- But we are given that the container has **15 ft³** of fertilizer after 5 weeks.
2. **Amount of fertilizer added in 14 more weeks**:
- For the next 14 weeks, the farm continues to deposit 1.5 ft³ each week:
\( 1.5 \, \text{ft}^3/\text{week} \times 14 \, \text{weeks} = 21 \, \text{ft}^3 \)
3. **Total fertilizer in the container after 19 weeks**:
- Initially in the container after 5 weeks: **15 ft³**
- Added during the next 14 weeks: **21 ft³**
- Total capacity of the container after 19 weeks:
\( 15 \, \text{ft}^3 + 21 \, \text{ft}^3 = 36 \, \text{ft}^3 \)
Thus, the capacity of the storage container is **36 ft³**.
The correct answer is **B. 36 ft³**.
1. **Amount of fertilizer after 5 weeks**:
- The farm deposits 1.5 ft³ of fertilizer each week.
- After 5 weeks:
\( 1.5 \, \text{ft}^3/\text{week} \times 5 \, \text{weeks} = 7.5 \, \text{ft}^3 \)
- But we are given that the container has **15 ft³** of fertilizer after 5 weeks.
2. **Amount of fertilizer added in 14 more weeks**:
- For the next 14 weeks, the farm continues to deposit 1.5 ft³ each week:
\( 1.5 \, \text{ft}^3/\text{week} \times 14 \, \text{weeks} = 21 \, \text{ft}^3 \)
3. **Total fertilizer in the container after 19 weeks**:
- Initially in the container after 5 weeks: **15 ft³**
- Added during the next 14 weeks: **21 ft³**
- Total capacity of the container after 19 weeks:
\( 15 \, \text{ft}^3 + 21 \, \text{ft}^3 = 36 \, \text{ft}^3 \)
Thus, the capacity of the storage container is **36 ft³**.
The correct answer is **B. 36 ft³**.