Question

The price of 3 chairs and 2 tables is 4500 rupees and price of 5 chairs and 3 tables is 7000 rupees, then find the price of 2 chairs and 2 tables.

Answer 1

Let the price of 1 chair be Rs x and the price of 1 table be Rs y.
The price of 3 chairs and 2 tables is 4500 rupees
$3x+2y=4500.....\left(\mathrm{I}\right)$
Price of 5 chairs and 3 tables is 7000 rupees
$5x+3y=7000.....\left(\mathrm{II}\right)$
Multiply (I) with 3 and (II) with 2
$$\begin{gathered} 9x+6y=13500.....\left(\mathrm{III}\right) \\ 10x+6y=14000.....\left(\mathrm{IV}\right) \\ \left(\mathrm{IV}\right)-\left(\mathrm{III}\right) \\ x=500 \\ \mathrm{Putting}\mathrm{this}\mathrm{value}\mathrm{of}x\mathrm{in}\left(\mathrm{I}\right) \\ 3\times 500+2y=4500 \\ \Rightarrow 1500+2y=4500 \\ \Rightarrow 2y=4500-1500=3000 \\ \Rightarrow y=1500 \end{gathered}$$
Price of 2 chairs and 2 tables will be
$$\begin{gathered} =2x+2y \\ =2\left(x+y\right) \\ =2\left(500+1500\right) \\ =2\times 2000 \\ =4000 \end{gathered}$$
Thus, the price of 2 chairs and 2 tables will be Rs 4000