Question

3 chairs and two tables cost rs700,while5 chairs and 3 tables cost rs 1100.what is the cost of 2 chairs and 2 tables?

Answer 1

Let the cost of 1 chair be ₹x and cost of 1 table be ₹y

So, case 1

Cost of 3 chairs will be ₹3x
Cost of 2 tables will be ₹2y

So,
3x + 2y = ₹700 ........(1)


Case 2

Cost of 5 chairs will be ₹5x
Cost of 3 tables will be ₹3y

So,
5x + 3y = ₹1100 .......(2)


In order to obtain the value of x and y , we have to solve the pair of linear equation in two variables.

I am going to solve this question by substitution method :-

From equation 1

3x + 2y = 700
Or,

2y = 700- 3x
Or,
y = (700 - 3x )/2

Putting this value of y in equation number 2
So,


5x + 3y = 1100
Putting the value of y we get :-

5x + 3{(700- 3x)/2} = 1100
Or,
5x + (2100- 9x)/2 = 1100
Or,
10x + 2100 - 9x = 1100*2
Or,
x = 2200 - 2100 = 100

So,

Cost of 1 chair is ₹100

Putting x= 100 in equation 1 to obtain the value of y

So,
3x + 2y = 700
Or,
3*100 + 2y = 700
2y = 700 - 300 = 400
or,
y = 400/2 = 200

So,
The cost of 1 table is ₹200


Now , cost of 2 chairs and 2 tables is 2x + 2y
So,
2x + 2y = 2*100 + 2*200 = 200+400 = ₹600