- Define the mean cost as the sum of all meal costs divided by 5: \(\frac{7.30 + 8.20 + 7.00 + x + 8.60}{5} = 7.30\).
- Multiply by 5 to find the total cost of all meals: \(7.30 + 8.20 + 7.00 + x + 8.60 = 36.50\).
- Simplify the sum of the known costs: \(31.10 + x = 36.50\).
- Calculate the final cost for the grilled fish meal: \(x = \boxed{\$5.40}\).
Explanation
- Analysis of the Problem
We are given the costs of five types of meals: Hamburger (\$7.30), Pizza (\$8.20), Steak (\$7.00), Grilled Fish (@@MATH_TOKEN_11@@), and Veggie (\$8.60). We know that the mean cost per meal for all five types is \$7.30. The mean of a set of values is calculated by taking the sum of all the values and dividing by the count of the values. Since there are five meals, the mean is defined as the sum of these five costs divided by 5.
- Setting Up and Simplifying the Equation
To find the value of \(x\), we first set up the equation for the mean:
\[ \text{Mean} = \frac{7.30 + 8.20 + 7.00 + x + 8.60}{5} = 7.30 \]
To isolate \(x\), we multiply both sides of the equation by 5:
\[ 7.30 + 8.20 + 7.00 + x + 8.60 = 7.30 \times 5 \]
\[ 7.30 + 8.20 + 7.00 + x + 8.60 = 36.50 \]
- Solving for the Cost of Grilled Fish
Next, we sum the known costs on the left side of the equation:
\[ 7.30 + 8.20 + 7.00 + 8.60 = 31.10 \]
So, our equation simplifies to:
\[ 31.10 + x = 36.50 \]
Subtracting 31.10 from both sides, we find:
\[ x = 36.50 - 31.10 \]
\[ x = 5.40 \]
Thus, the cost per meal for the grilled fish is \$5.40.
Examples
Understanding how to calculate a mean is essential in everyday life. For example, if you are tracking your monthly food expenses, knowing the average cost of your meals helps you budget effectively. If you know how much you have spent on most of your meals and what your overall target average cost is, you can determine how much you should spend on your remaining meals to stay within your budget. Similar methods are used in finance, sports statistics, and inventory management to analyze performance and cost-efficiency.