3 chairs and 2 table cost of rupees 1850 and 5 chairs and 3 tables cost of rupees 2850 find the cost of rupees 2 chairs and 2 tables
Answers
Answer:
The cost of 2 chairs and 2 tables is ₹ 1700
Step-by-step explanation:
Let, cost of each chair be ₹ x and cost of each table be ₹ y.
Case I : Cost of 3 chairs and 2 tables is ₹ 1850
3 chairs + 2 tables = ₹ 1850
==> 3x + 2y = 1850 —————— (i)
Case II : Cost of 5 chairs and 3 tables is ₹ 2850
5 chairs + 3 tables = ₹ 2850
==> 5x + 3y = 1850 —————— (ii)
Equation (i) × 3 and equation (ii) × 2 gives
9x + 6y = 5550 —————— (iii)
10x + 6y = 5700 —————— (iv)
Equation (iv) - equation (iii) gives
x = 150
Now, after substituting x = 150 in Equation (i) we get
3( 150 ) + 2y = 1850
==> 2y = 1850 - 450
==> y = 1400 / 2
==> y = 700
∴ x = 150 and y = 700
Therefore, cost of each chair = x = ₹ 150 and cost of each table = y = ₹ 700
As per the question,
Cost of 2 chairs + Cost of 2 tables = 2x + 2y = 2( x + y )
= ₹ 2( 150 + 700 )
= ₹ 2( 850 )
= ₹ 1700
Hence, the cost of 2 chairs and 2 tables is ₹ 1700