Twelve friends raised some funds among themseleve for a dinner party. Ten of the contributed $80 each while the other two subscrible $80 and $120 more than the average of all twelve friends . What was the average contribution of all the friends taken together ?

Options

A. 220
B. 180
C. 100
D. 80

Answer

To find the average contribution of all twelve friends, we can break down the problem step by step.

### Step 1: Define the average contribution
Let the average contribution of all twelve friends be denoted as \( x \). Since there are twelve friends, the total contribution can be expressed as:
\[ \text{Total Contribution} = 12x \]

### Step 2: Calculate contributions from the first ten friends
Ten of the friends contributed $80 each. Therefore, the total contribution from these ten friends is:
\[ \text{Total from 10 friends} = 10 \times 80 = 800 \]

### Step 3: Contributions from the other two friends
The other two friends contributed amounts that are above the average \( x \):
- The first friend contributed \( x + 80 \) (which is $80 more than the average).
- The second friend contributed \( x + 120 \) (which is $120 more than the average).

Thus, the total contribution from these two friends is:
\[ \text{Total from 2 friends} = (x + 80) + (x + 120) = 2x + 200 \]

### Step 4: Combine total contributions
Now, we can combine the contributions from all twelve friends:
\[ \text{Total Contribution} = \text{Total from 10 friends} + \text{Total from 2 friends} \]
Substituting the values we calculated:
\[ 12x = 800 + (2x + 200) \]

### Step 5: Simplify the equation
Now, simplify the equation:
\[ 12x = 800 + 2x + 200 \]
\[ 12x = 1000 + 2x \]

### Step 6: Solve for \( x \)
To isolate \( x \), subtract \( 2x \) from both sides:
\[ 12x - 2x = 1000 \]
\[ 10x = 1000 \]
Now, divide both sides by 10:
\[ x = \frac{1000}{10} = 100 \]

### Conclusion
The average contribution of all twelve friends taken together is:
\[ \boxed{100} \]

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