According to a plan, a team of woodcutters decided to harvest 216 m3 of wheat in several days. In the first three days, the team fulfilled the daily assignment, and then it harvested 8 m3 of wheat over and above the plan every day. Therefore, a day before the planned date, they had already harvested 232 m3 of wheat.
How many cubic metres of wheat a day did the team have to cut according to the plan?

Options

A. A)24
B. B)28
C. C)26
D. D)Can't be determined

Answer

To solve the problem step by step, we will denote the daily assignment of wheat that the team had to cut according to the plan as \( K \) cubic meters per day. The total amount of wheat to be harvested is 216 m³.

### Step 1: Set up the equations
The total amount of wheat harvested according to the plan over \( t \) days is given by:
\[ K \times t = 216 \]

### Step 2: Analyze the harvesting over the days
In the first three days, the team harvested according to the plan, which means:
\[ \text{Wheat harvested in first 3 days} = 3K \]
After the first three days, they harvested 8 m³ more than the planned amount each day. Therefore, for the remaining \( t - 3 \) days, they harvested:
\[ \text{Wheat harvested in remaining days} = (K + 8)(t - 3) \]

### Step 3: Total wheat harvested
The total wheat harvested over the entire period is:
\[ 3K + (K + 8)(t - 3) = 232 \]
This equation states that the total harvested wheat is 232 m³, which is 16 m³ more than the planned amount of 216 m³.

### Step 4: Expand the equation
Now, we can expand the equation:
\[ 3K + (K + 8)(t - 3) = 232 \]
Expanding gives:
\[ 3K + K(t - 3) + 8(t - 3) = 232 \]
This simplifies to:
\[ 3K + Kt - 3K + 8t - 24 = 232 \]
Thus, we have:
\[ Kt + 8t - 24 = 232 \]

### Step 5: Substitute \( Kt = 216 \)
From the first equation, we know:
\[ Kt = 216 \]
Substituting this into the equation gives:
\[ 216 + 8t - 24 = 232 \]
Simplifying this results in:
\[ 8t + 192 = 232 \]
\[ 8t = 232 - 192 \]
\[ 8t = 40 \]
\[ t = 5 \]

### Step 6: Substitute \( t \) back to find \( K \)
Now that we have \( t = 5 \), we can substitute back to find \( K \):
\[ K \times 5 = 216 \]
\[ K = \frac{216}{5} = 43.2 \]

### Step 7: Check the results
However, we need to check if this value of \( K \) is consistent with the harvesting conditions. Since the team harvested 8 m³ over the plan after the first three days, we can check:
- In the first 3 days: \( 3K = 3 \times 43.2 = 129.6 \)
- In the next 2 days (5 - 3 = 2): \( (K + 8) \times 2 = (43.2 + 8) \times 2 = 51.2 \times 2 = 102.4 \)

Total harvested:
\[ 129.6 + 102.4 = 232 \]
This confirms our calculations.

### Conclusion
Thus, the daily assignment of wheat that the team had to cut according to the plan is:
\[ \boxed{43.2} \text{ cubic meters per day} \]