https://file.aiquickdraw.com/mathbot/file/1727104822584d934bazf.jpg

Let's break down the problem based on the image provided:

We are given:

- **x** is the cost to rent a chair (in dollars).
- **y** is the cost to rent a table (in dollars).
- Two customers, with different numbers of chairs and tables rented, and their total costs:

|            | Number of Chairs | Number of Tables | Total Cost |
|------------|------------------|------------------|------------|
| First      | 12               | 2                | $43        |
| Second     | 3                | 5                | $40        |

### (a) System of Equations

For the first customer:
- They rented 12 chairs and 2 tables, so the total cost equation will be:
\[
12x + 2y = 43
\]

For the second customer:
- They rented 3 chairs and 5 tables, so the total cost equation will be:
\[
3x + 5y = 40
\]

### (b) Solving for the cost of each chair and each table:

We can solve the system of equations to find the values of $x$ and $y$.

The system of equations is:

1. $12x + 2y = 43$
2. $3x + 5y = 40$

Let me solve this system for you.The solution to the system of equations is:

- Cost to rent each chair ($x$) = $ \frac{5}{2} = 2.5$ dollars
- Cost to rent each table ($y$) = $ \frac{13}{2} = 6.5$ dollars

Would you like more details on how this solution was derived or any further explanation?

Here are some related questions:
1. What method can be used to solve systems of equations algebraically?
2. How do you verify the solution to a system of equations?
3. Can this system of equations be solved using matrices?
4. What if the total cost was different for the second customer—how would it change the solution?
5. How can substitution be used to solve the system of equations?

**Tip:** When solving systems of equations, make sure to check the solution by substituting the values back into the original equations.

Write a system of equations to find the rental cost (in dollars) of each chair and each table, and determine the cost of each chair and table based on the number of chairs and tables rented by two customers.

Learn how to solve a system of linear equations to find the rental cost of chairs and tables. This problem involves two customers renting different numbers of chairs and tables, leading to a system of equations for determining individual costs. Suitable for students in Grades 7-10.

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