https://file.aiquickdraw.com/mathbot/file/17325039947181y2zj6d9.jpg

From the image, we can break down the word problem and solve it using a system of linear equations.

### Problem Breakdown:
Keisha owns three food stands, each selling apples, cherries, and pears. The table gives the number of bags sold at each location. We also know the revenue generated from each stand:
- **Tomsville**: $77
- **Newbury Heights**: $67
- **Glen City**: $43

Let:
- $ x $ = cost of a bag of apples
- $ y $ = cost of a bag of cherries
- $ z $ = cost of a bag of pears

The equations can be written as:
1. $ 6x + 2y + z = 77 $ (Tomsville revenue equation)
2. $ x + 5y + z = 67 $ (Newbury Heights revenue equation)
3. $ 2x + y + 8z = 43 $ (Glen City revenue equation)

We need to solve this system of equations for $ x $, $ y $, and $ z $.

### Step 1: Solve the system of equations
Let me compute this.from sympy import symbols, Eq, solve

# Define the variables
x, y, z = symbols('x y z')

# Define the equations based on the problem
eq1 = Eq(6*x + 2*y + z, 77)  # Tomsville equation
eq2 = Eq(x + 5*y + z, 67)    # Newbury Heights equation
eq3 = Eq(2*x + y + 8*z, 43)  # Glen City equation

# Solve the system of equations
solution = solve((eq1, eq2, eq3), (x, y, z))
solution{x: 623/71, y: 2405/213, z: 377/213}{x: 623/71, y: 2405/213, z: 377/213}successThe solution to the system of equations is as follows:

- Cost of a bag of apples ($x$): $\frac{623}{71} \approx 8.77$
- Cost of a bag of cherries ($y$): $\frac{2405}{213} \approx 11.29$
- Cost of a bag of pears ($z$): $\frac{377}{213} \approx 1.77$

If you'd like, I can further clarify or double-check any part of the solution. Let me know! 

### Related Questions:
1. How can you verify the solution to this problem using substitution?
2. What happens if you change one of the revenue values? How does it affect the solution?
3. How would this problem change if the prices of the items were given instead of the revenue?
4. Can this problem be solved graphically, and what would the process look like?
5. What are other methods to solve a system of equations like this (e.g., elimination)?

### Tip:
Always double-check your solutions by substituting them back into the original equations to ensure they satisfy all conditions.

Keisha owns three food stands, each selling apples, cherries, and pears. The revenue and number of bags sold for each item at the three stands are provided in a table. If the revenue from Tomsville is $77, Newbury Heights is $67, and Glen City is $43, what is the cost of each bag of apples, cherries, and pears?

Learn how to solve a system of linear equations to find the cost of apples, cherries, and pears sold at food stands. This problem involves calculating costs based on revenue and quantities sold, using algebraic methods suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation