Question

4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750. Find the cost of 1 table and 1 chair separately.

Answer 1

Hint: Now to solve the given problem we will assume the cost of one chair to be x and the cost of one table to be y. Now we will form equations with the help of given conditions. Hence we will solve the two equations simultaneously to find the values of x and y.

Complete step by step solution:
Now let the cost of one chair be x and the cost of 1 table be y.
Now we know that the cost of 4 chairs will be 4x and the cost of 3 tables will be 3y.
We are given that the cost of three tables and 4 chairs is Rs 2100.
Hence we can write this in the equation as 4x + 3y = 2100.
Let $4x+3y=2100............\left( 1 \right)$ .
Now again we know that the cost of 5 chairs is 5x and the cost of 2 tables is 2y.
Now we know that the cost of 5 chairs and 2 tables is Rs 1750.
Hence in equation form we can write it as 5x + 2y = 1750.
Let $5x+2y=1750........\left( 2 \right)$
Now let us multiply equation (1) by 2 and the equation (2) by 3.
Hence we get,
$8x+6y=4200............\left( 3 \right)$
$15x+6y=5250..........\left( 4 \right)$
Now let us subtract equation (3) from equation (4) Hence we get,
\[\begin{align}
  & \Rightarrow 15x-8x+6y-6y=5250-4200 \\
 & \Rightarrow 7x=1050 \\
 & \Rightarrow x=150 \\
\end{align}\]
Hence we get the value of x is 150.
Now substituting the value of x in equation (1) we get,
$\begin{align}
  & \Rightarrow 4\left( 150 \right)+3y=2100 \\
 & \Rightarrow 600+3y=2100 \\
 & \Rightarrow 3y=2100-600 \\
 & \Rightarrow 3y=1500 \\
 & \Rightarrow y=500 \\
\end{align}$
Hence we have the value of y = 500.
Hence the cost of one chair is 150 Rs and the cost of one table is 500 Rs.

Note: Now let the cost of one chair be x and the cost of 1 table be y.
Now we know that the cost of 4 chairs will be 4x and the cost of 3 tables will be 3y.
We are given that the cost of three tables and 4 chairs is Rs 2100.
Hence we can write this in the equation as 4x + 3y = 2100.
Let $4x+3y=2100............\left( 1 \right)$ .
Now again we know that the cost of 5 chairs is 5x and the cost of 2 tables is 2y.
Now we know that the cost of 5 chairs and 2 tables is Rs 1750.
Hence in equation form we can write it as 5x + 2y = 1750.
Let $5x+2y=1750........\left( 2 \right)$
Now let us multiply equation (1) by 2 and the equation (2) by 3.
Hence we get,
$8x+6y=4200............\left( 3 \right)$
$15x+6y=5250..........\left( 4 \right)$
Now let us subtract equation (3) from equation (4) Hence we get,
\[\begin{align}
  & \Rightarrow 15x-8x+6y-6y=5250-4200 \\
 & \Rightarrow 7x=1050 \\
 & \Rightarrow x=150 \\
\end{align}\]
Hence we get the value of x is 150.
Now substituting the value of x in equation (1) we get,
$\begin{align}
  & \Rightarrow 4\left( 150 \right)+3y=2100 \\
 & \Rightarrow 600+3y=2100 \\
 & \Rightarrow 3y=2100-600 \\
 & \Rightarrow 3y=1500 \\
 & \Rightarrow y=500 \\
\end{align}$
Hence we have the value of y = 500.
Hence the cost of one chair is 150 Rs and the cost of one table is 500 Rs.