Question

The cost of 4 chairs and 3 table is rs 2100. where as that of 5 chairs and 2 table is rs 1750. find the cost of a chair and a table.

Answer 1

kutlehria8899 Yesterday
Your answer
(QUIT)
strangechanakyaHelping Hand

Let the cost of one chair be Rs. X and the cost of one table be Rs. Y
Now, cost of 4 chairs and 3 tables is Rs. 2100 I.e. 4X+3Y = 2100 --1
and cost of 5 chairs and 2 tables is 1750 i.e. 5X + 2Y = 1750 --2
Solving
Multiply equation 1 by 2
8X + 6Y = 4200 --3
Multiply equation 2 by 3
15X + 6Y = 5250 --4
Now substract equation 3 from equation 4
15X + 6Y - 8X - 6Y = 5250 - 4200
7X = 1050
X = 150
Put this value of X in 1
4×150 + 3Y =2100
3Y = 2100 - 600
3Y = 1500
Y = 500 therefore cost of one chair is
Rs. 150 and cost of one table is Rs. 500

Answer 2

Given data : 4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750.

Solution : Let, the cost of one chair be x and the cost of one table be y.

Now, according to the given data;

• 4x + 3y = 2100 ----{1}

• 5x + 2y = 1750 ----{2}

Now, multiply eq. {1} by 2

• 8x + 6y = 4200 ----{3} and similarly,

Multiply eq. {2} by 3

• 15x + 6y = 5250 ----{4}

Now, subtract eq. {3} from eq. {4}

15x + 6y = 5250

- (8 + 6y) = 4200

______________

7x = 1050

x = 1050/7

x = 150

Now, put value of x in eq. {1}

➜ 4x + 3y = 2100

➜ 4*(150) + 3y = 2100

➜ 600 + 3y = 2100

➜ 3y = 2100 - 600

➜ 3y = 1500

➜ y = 1500/3

➜ y = 500

Answer : Hence, the cost of one chair is Rs 150 and the cost of one table is Rs 500.

[Verification : Put vale of x and y in eq. {1}

➜ 4x + 3y = 2100

➜ 4*(150) + 3*(500) = 2100

➜ 600 + 1500 = 2100

➜ 2100 = 2100

Hence, it's verified]