Question

A chair and 4 tables together cost Rs.5600, while 4 chairs and 3 tables together cost Rs.4340.Find the cost of each chair and that of each table

Answer 1

Answer :

$\large \underline{\boxed{\textsf{Cost of a Chair = 43.04 rs and Cost of table = 1389.24 }}}$

Step-by-step explanation

$\underline{\underline{\large{\textbf{Given that...}}}}$

A chair and 4 tables together cost Rs.5600, while 4 chairs and 3 tables together cost Rs.4340.

Now weed need to find the cost of each chair and table..

$\underline{\underline{\large{\textbf{Solution...}}}}$

Let the cost of ,

One chair = x }------ 1

One table = y }------ 2

Now According to Question

A chair and 4 tables together cost Rs.5600, while 4 chairs and 3 tables together cost Rs.4340.

That is

$\implies$ A chair + 4 tables = ₹5600

and

$\implies$ 4 chairs + 3 tables = ₹4340

Therefore from eq 1 and 2 we have

$\implies \mathsf{x + 4y = 5600}$ -------- (¡)

$\implies \mathsf{4x + 3y = 4340}$ ------- (¡¡)

From Equation (¡) we have

$\mathsf{x = 5600-4y}$------- (iii)

Putting value of x = 5600-4y in equation (¡¡) we have

$\mathsf{4(5600-4y) + 3y = 4340}$

$\implies \mathsf{22,400-16y +3y = 4340}$

$\implies \mathsf{22,400-13y = 4340}$

$\implies \mathsf{-13y = 4340-22,400}$

$\implies \mathsf{13y = 18,060}$

$\implies \mathsf{y = \dfraf{18,060}{13}\: =1389.\overline{230769} \approx 1389.24\: rs}$

Now putting value of y = 1389.24 in eq (iii) we have

$\mathsf{x = 5600-4(1389.24)}$

$\mathsf{x = 43.04rs}$

Therefore we have Cost of

Chair = x = ₹ 43.04

Table = y = ₹ 1389.24

Answer 2

Answer:

cost of chair = Rs 43.08

Cost of table = Rs 1389.23

Step-by-step explanation:

let price of chair be x

and that of table be y

ATQ,

x + 4y = 5600

x = 5600 - 4y. ....(1)

and

4x + 3y = 4340. ....(2)

4(5600 - 4y) + 3y = 4340

22400 - 16y + 3y = 4340

-13y = 4340 - 22400

y = -18060/-13

y = 1389.23 (approx)

From (1)

x = 5600 - 4y

x = 5600 - 4(1389.23)

x = 5600 - 5556.92

x = 43.08

so,

cost of chair = Rs 43.08

Cost of table = Rs 1389.23