Nine friends have a dinner in a hotel. Eight of them spent X 12 each on their meals and the ninth spent X 16 more than the average expenditure of all the nine. Find out the total money spent by them.

Options

A. X126
B. X135
C. X111
D. X141

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the total amount spent by the first eight friends.
The first eight friends each spent X 12. Therefore, the total amount spent by these eight friends is:
\[ \text{Total spent by 8 friends} = 8 \times 12 = 96 \]

### Step 2: Define the average expenditure of all nine friends.
Let the average expenditure of all nine friends be denoted as \( A \).

### Step 3: Determine the expenditure of the ninth friend.
According to the problem, the ninth friend spent X 16 more than the average expenditure. Therefore, the expenditure of the ninth friend can be expressed as:
\[ \text{Expenditure of 9th friend} = A + 16 \]

### Step 4: Set up the equation for the total expenditure.
The total expenditure of all nine friends can be expressed as:
\[ \text{Total expenditure} = \text{Total spent by 8 friends} + \text{Expenditure of 9th friend} \]
Substituting the values we have:
\[ \text{Total expenditure} = 96 + (A + 16) = 96 + A + 16 = 112 + A \]

### Step 5: Relate total expenditure to average expenditure.
The total expenditure can also be expressed in terms of the average expenditure \( A \):
\[ \text{Total expenditure} = 9A \]

### Step 6: Set the two expressions for total expenditure equal to each other.
Now we can set the two expressions for total expenditure equal:
\[ 112 + A = 9A \]

### Step 7: Solve for \( A \).
Rearranging the equation gives:
\[ 112 = 9A - A \]
\[ 112 = 8A \]
\[ A = \frac{112}{8} = 14 \]

### Step 8: Calculate the total money spent by all nine friends.
Now that we have the average expenditure, we can find the total money spent by all nine friends:
\[ \text{Total money spent} = 9A = 9 \times 14 = 126 \]

### Final Answer:
The total money spent by the nine friends is \( \text{X} 126 \).

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