It rained as much as Wednesday as on all the other days of the week combined .If the average rainfall for the whole week was 3 cm , how much did it rain on Wednesday ?

Options

A. 2.625 cm
B. 3 cm
C. 10. 5 cm
D. 15 cm

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the Problem
We know that it rained as much on Wednesday as it did on all the other days combined. We also know that the average rainfall for the whole week is 3 cm.

### Step 2: Calculate Total Rainfall for the Week
Since there are 7 days in a week and the average rainfall is 3 cm, we can calculate the total rainfall for the week using the formula for average:
\[ \text{Total Rainfall} = \text{Average Rainfall} \times \text{Number of Days} \]
\[ \text{Total Rainfall} = 3 \, \text{cm} \times 7 = 21 \, \text{cm} \]

### Step 3: Set Up the Equation
Let \( x \) be the amount of rain on Wednesday. According to the problem, the rain on Wednesday is equal to the rain on all other days combined. Therefore, we can express the total rainfall as:
\[ x + (21 - x) = 21 \]
This simplifies to:
\[ x + (21 - x) = x + 21 - x = 21 \]
This means that the rainfall on Wednesday is equal to the total rainfall minus the rainfall on Wednesday itself.

### Step 4: Solve for \( x \)
Since we know that the total rainfall for the week is 21 cm, and the rainfall on Wednesday is equal to the sum of the rainfall on the other 6 days, we can set up the equation:
\[ x = 21 - x \]
Adding \( x \) to both sides gives us:
\[ 2x = 21 \]
Now, divide both sides by 2:
\[ x = \frac{21}{2} = 10.5 \, \text{cm} \]

### Step 5: Conclusion
Thus, the amount of rain on Wednesday is 10.5 cm.

### Final Answer:
It rained **10.5 cm** on Wednesday.

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