The mean number of tickets sold daily by a theater over a seven - day period was 52. The theater sold 46 tickets on the last day of that period. What was the mean number of tickets sold daily over the first six days ?

Options

A. 53
B. 54
C. 55
D. 56

Explanation

To find the mean number of tickets sold daily over the first six days, we can follow these steps:

### Step 1: Calculate the total number of tickets sold over the seven days.
The mean number of tickets sold daily over a seven-day period is given as 52. To find the total number of tickets sold over the seven days, we multiply the mean by the number of days:

\[ \text{Total tickets sold in 7 days} = \text{Mean} \times \text{Number of days} = 52 \times 7 \]

Calculating this gives:

\[ 52 \times 7 = 364 \]

### Step 2: Determine the number of tickets sold in the first six days.
We know that on the last day (the seventh day), 46 tickets were sold. To find the number of tickets sold in the first six days, we subtract the tickets sold on the last day from the total tickets sold in the seven days:

\[ \text{Tickets sold in first 6 days} = \text{Total tickets sold} - \text{Tickets sold on last day} = 364 - 46 \]

Calculating this gives:

\[ 364 - 46 = 318 \]

### Step 3: Calculate the mean number of tickets sold over the first six days.
To find the mean number of tickets sold over the first six days, we divide the total number of tickets sold in the first six days by the number of days (which is 6):

\[ \text{Mean tickets sold in first 6 days} = \frac{\text{Tickets sold in first 6 days}}{\text{Number of days}} = \frac{318}{6} \]

Calculating this gives:

\[ \frac{318}{6} = 53 \]

### Final Answer:
The mean number of tickets sold daily over the first six days is **53**.

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