Cost of Tables and Chairs

Video Explanation

Question

4 tables and 3 chairs together cost Rs 2250 and 3 tables and 4 chairs cost Rs 1950. Find the cost of 2 chairs and 1 table.

Solution

Step 1: Let the Variables

Let the cost of 1 table = Rs \(x\)

Let the cost of 1 chair = Rs \(y\)

Step 2: Form the Equations

\[ 4x + 3y = 2250 \quad (1) \]

\[ 3x + 4y = 1950 \quad (2) \]

Step 3: Solve by Elimination Method

Multiply equation (1) by 4:

\[ 16x + 12y = 9000 \quad (3) \]

Multiply equation (2) by 3:

\[ 9x + 12y = 5850 \quad (4) \]

Subtract (4) from (3):

\[ 7x = 3150 \]

\[ x = 450 \]

Step 4: Find the Value of y

Substitute \(x = 450\) in equation (1):

\[ 4(450) + 3y = 2250 \]

\[ 1800 + 3y = 2250 \]

\[ 3y = 450 \]

\[ y = 150 \]

Step 5: Find Cost of 2 Chairs and 1 Table

\[ x + 2y = 450 + 2(150) \]

\[ = 450 + 300 \]

\[ = 750 \]

Conclusion

Cost of 2 chairs and 1 table:

\[ \boxed{Rs\;750} \]