Question

If 2 tables and 3 chairs cost Rs. 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost?​

Answer 1

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Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.

Then, 2x + 3y = 3500 ...(i)

and 3x + 2y = 4000 ...(ii)

solving (i) and (ii) we get x = 1000, y = 500

Answer 2

Given: Cost of 2 tables and 3 chairs = Rs. 3,500

           Cost of 3 tables and 2 chairs = Rs. 4,000

To find: Cost of one table

Let: Cost of one table be $x$ and cost of one chair be $y$

Solution: According to the given question and assumption made,

$2x + 3y = 3500$   ...(1)

also, $3x + 2y = 4000$    ...(2)

Solving the above equations using elimination method:

LCM of coefficients of $x$ (2 and 3) = 6

Multiplying equation (1) by 3

⇒ $6x + 9y = 10500$ ...(3)

Multiplying equation (2) by 2

⇒ $6x + 4y = 8000$   ...(4)

Subtracting equation (4) from equation (3)

⇒ $(6x + 9y) - (6x + 4y) = 10500 - 8000$

⇒ $6x + 9y - 6x - 4y = 2500$

⇒ $5y = 2500$

⇒ $y = \frac{2500}{5} = 500$

Putting $y = 500$ in equation (2)

⇒ $3x + 2(500) = 4000$

⇒ $3x + 1000 = 4000$

⇒ $3x = 3000$

⇒ $x = \frac{3000}{3} = 1000$

Hence, a table costs Rs. 1,000 ($x$).