Let's solve the problem step by step, organizing our information in a table and then moving towards a solution.
First, we'll categorize the number of people and the prices of their meals.
| Meal Price (\[tex]$) | Number of People |
|-----------------|------------------|
| 15 | 2 |
| 17 | 2 |
| 13 | 3 |
| 14 | 3 |
### Step 1: Calculate the total number of people
To find the total number of people attending the dinner party, we sum up the number of people in each category:
\[
2 \text{ (price \$[/tex]15)} + 2 \text{ (price \[tex]$17)} + 3 \text{ (price \$[/tex]13)} + 3 \text{ (price \[tex]$14)} = 10
\]
### Step 2: Calculate the total cost of all meals
Next, we calculate the total cost of the meals by multiplying the number of people by the price of their meals and summing these products:
\[
(2 \times 15) + (2 \times 17) + (3 \times 13) + (3 \times 14)
\]
Breaking it down:
\[
2 \times 15 = 30 \\
2 \times 17 = 34 \\
3 \times 13 = 39 \\
3 \times 14 = 42
\]
Adding these values together:
\[
30 + 34 + 39 + 42 = 145
\]
### Step 3: Calculate the average price per meal
To find the average price per meal, we divide the total cost by the total number of people:
\[
\text{Average price} = \frac{\text{Total cost}}{\text{Total number of people}} = \frac{145}{10} = 14.5
\]
Thus, the average price of each meal is \$[/tex]14.5.
