3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens toget

1.	3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. Find the total cost of 1 bag and 10 pens.
Answer» Let the cost of 1 bag be ‘a’ and 1 pen be ‘b’. Given, 3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. ⇒ 3a + 4b = 257 ----------- (1) and 4a + 3b = 324 ---------- (2) Multiplying eq1 by 4 and eq2 by 3 and subtracting eq2 from eq1. ⇒ 12a + 16b – 12a – 9b = 1028 – 972 ⇒ 7b = 56 ⇒ b = Rs. 8 Substituting in eq1 ⇒ 3a + 32 = 257 ⇒ a = Rs. 75 Cost of 1 bag and 10 pens = 75 + 10 × 8 = Rs. 155

3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. Find the total cost of 1 bag and 10 pens.

Answer»

Let the cost of 1 bag be ‘a’ and 1 pen be ‘b’.

Given,

3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324.

⇒ 3a + 4b = 257 ----------- (1)

and 4a + 3b = 324 ---------- (2)

Multiplying eq1 by 4 and eq2 by 3 and subtracting eq2 from eq1.

⇒ 12a + 16b – 12a – 9b = 1028 – 972

⇒ 7b = 56

⇒ b = Rs. 8

Substituting in eq1

⇒ 3a + 32 = 257

⇒ a = Rs. 75

Cost of 1 bag and 10 pens = 75 + 10 × 8 = Rs. 155