The cost of 4 chairs hantdhree table is 2100. And cost of 5 chair and 2 tables is Really 1750.find the cost of 1 chair and 1 table seperately
Answers
so cost of 1 chair is 150 rupees and
cost of 1 table is 500 rupees
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]