5 chairs and 4 tables together cost Rs. 5,600, while 4 chairs and 3 tables together cost Rs. 4340. Find the cost of a chair and that of a table.

Class 10 > R S Aggarwal > Linear Equation in two variables > Word Problems

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 Question: 5 chairs and 4 tables together cost Rs. 5,600, while 4 chairs and 3 tables together cost Rs. 4340. Find the cost of one chair and that of one table.

Solution: 

Let the Cost of 1 chair and 1 table be Rs. x and y respectively.
Then cost of 5 chairs and 4 tables becomes 5x and 4y while the price of 4 chairs and 3 tables becomes 4x and 3y respectively.

A/q: 5x + 4y = 5600     .............(i)
        4x + 3y = 4340     .............(ii)

A problem on Linear Equation in Two Variables can be solved either by substitution method or elimination method or cross multiplication method.

Here we will solve it using Substitution method.

From eq. (i), we get  y = (5600 - 5x)/4    .........(iii)
Substituting this value in equation in (ii)

4x + 3{(5600 - 5x)/4} = 4340

4x + {(16800 - 15x)/4} = 4340

Solving it:

(16x + 16800 - 15x)/4 = 4340

(x + 16800)/4 = 4340

x + 16800 = 17360

x = 17360 - 16800

x = Rs. 560

Substituting this value of x to get the value of y in eq. (iii)

y = {5600 - 5(560)}/4

y = (5600 - 2800)/4

y = Rs. 700

Therefore, cost of 1 chair = Rs. 560 and that of 1 table = Rs. 700

The above question has been taken from the R S Aggarwal Book and form the Chapter 3 of Exercise 3E and has been used for educational purpose.

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