if two tables and two chairs cost 30$ and three tables and four chair cost 50$ . find the cost of a table and a chair

Let's define the variables as follows:

- Let $ x $ represent the cost of one table.
- Let $ y $ represent the cost of one chair.

Based on the problem:

1. Two tables and two chairs cost $30. This gives us the equation:
   \[
   2x + 2y = 30
   \]

2. Three tables and four chairs cost $50. This gives us the second equation:
   \[
   3x + 4y = 50
   \]

### Step 1: Simplify the first equation
Dividing the first equation by 2:
\[
x + y = 15
\]

### Step 2: Solve the system of equations
Now, we have the system of equations:
1. $ x + y = 15 $
2. $ 3x + 4y = 50 $

#### Substitution method:
From the first equation, solve for $ x $:
\[
x = 15 - y
\]

Substitute this expression for $ x $ in the second equation:
\[
3(15 - y) + 4y = 50
\]

Simplifying:
\[
45 - 3y + 4y = 50
\]
\[
45 + y = 50
\]
\[
y = 5
\]

### Step 3: Find the value of $ x $
Substitute $ y = 5 $ into $ x + y = 15 $:
\[
x + 5 = 15
\]
\[
x = 10
\]

### Conclusion:
The cost of one table is **$10** and the cost of one chair is **$5**.

Do you need more details or have any questions? Here are some related questions to explore further:

1. How would the solution change if two tables and four chairs cost $40?
2. What is the total cost for five tables and six chairs?
3. If the cost of chairs doubled, how would the equations change?
4. How can you solve this using matrix methods?
5. Can you generalize this method to solve for any number of items?

**Tip**: When solving systems of equations, both substitution and elimination methods can be useful, so choose based on simplicity.

If two tables and two chairs cost $30 and three tables and four chairs cost $50, find the cost of a table and a chair.

Discover how to solve a system of equations to find the cost of one table and one chair. Two tables and two chairs cost $30, while three tables and four chairs cost $50. This algebra problem uses substitution to provide a step-by-step solution for students in Grades 6-8.

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