The IKEA Store made a special promotion where the price of a set of 7 chairs and 13 tables would cost $1060 while the price of 13 chairs and 7 tables would be $940. If all chairs and tables are identical, what is the combined cost of of two chairs and one table ?

Options

A. 40
B. 60
C. 100
D. 140

Answer

To solve the problem, we will set up a system of equations based on the information given about the prices of chairs and tables.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( x \) be the price of one chair and \( y \) be the price of one table.

2. **Set Up Equations**:
From the problem, we have two pieces of information:
- The cost of 7 chairs and 13 tables is $1060:
\[ 7x + 13y = 1060 \quad \text{(Equation 1)} \]
- The cost of 13 chairs and 7 tables is $940:
\[ 13x + 7y = 940 \quad \text{(Equation 2)} \]

3. **Add the Two Equations**:
We can add Equation 1 and Equation 2 to eliminate \( y \):
\[ (7x + 13y) + (13x + 7y) = 1060 + 940 \]
This simplifies to:
\[ 20x + 20y = 2000 \]

4. **Simplify the Equation**:
Divide the entire equation by 20:
\[ x + y = 100 \quad \text{(Equation 3)} \]

5. **Express \( y \) in Terms of \( x \)**:
From Equation 3, we can express \( y \):
\[ y = 100 - x \]

6. **Substitute \( y \) in Equation 2**:
Substitute \( y \) in Equation 2:
\[ 13x + 7(100 - x) = 940 \]
Simplifying this gives:
\[ 13x + 700 - 7x = 940 \]
Combine like terms:
\[ 6x + 700 = 940 \]

7. **Solve for \( x \)**:
Subtract 700 from both sides:
\[ 6x = 240 \]
Divide by 6:
\[ x = 40 \]

8. **Find \( y \)**:
Substitute \( x \) back into Equation 3:
\[ y = 100 - 40 = 60 \]

9. **Calculate the Combined Cost of Two Chairs and One Table**:
We need to find the cost of 2 chairs and 1 table:
\[ 2x + y = 2(40) + 60 \]
Calculate:
\[ 80 + 60 = 140 \]

### Final Answer:
The combined cost of two chairs and one table is **$140**.