Question

4 chairs and 3 tables cost 2100 and 5 chairs and 2 tables cost 1750. Find the cost of one chair and one table seprately

Answer 1

Here's your answer mate



Let the cost of one chair be as x
Let the cost of one table be as y

According to first conditions

4x + 3y = 2100............... Eq1

According to 2 conditions

5x + 2y = 1750............... Eq2


Multiplying eq1 by 2 and eq2 by 3

2(4x + 3y = 2100)
8x + 6y = 4,200...........eq3

3(5x + 2y = 1750)
15x+ 6y =5,250........ eq4


Subtracting eq4 by eq3

15x+ 6y = 5,250
8x + 6y = 4,200
- - -
7x = 1,050

$x = \frac{1050}{7}$
$x = 150$



Taking x= 150 in eq1

4x +3y = 2100
4(150) + 3y =2100
600 + 3y = 2100
3y = 2100- 600
3y = 1500

$y = \frac{1500}{3}$
y= 500



Therefore, cost of one chair = x = 150
& cost of one table = y = 500



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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]