3 bags and 4 pens together cost ₹ 257 whereas 4 bags and 3 pens toge

1.	3 bags and 4 pens together cost ₹ 257 whereas 4 bags and 3 pens together cost ₹324. Find the total cost of 1 bag and 10 pens.
Answer» Let the cost of a bag and a pen be ₹ x and ₹ y, respectively. Then, according to the question 3x + 4y = 257 … (i) 4x + 3y = 324 … (ii) On multiplying equation (i) by 3 and (ii) by 4, We get, 9x + 12y = 770 … (iii) 16x + 12y = 1296 … (iv) Subtracting equation (iii) from (iv), we get 16x – 9x = 1296 – 771 7x = 525 x = 525/7 = 75 Hence, the cost of a bag = ₹ 75 Substituting x = 75 in equation (i), We get, 3 x 75 + 4y = 257 225 + 4y = 257 4y = 257 – 225 4y = 32 y = 32/4 = 8 Hence, the cost of a pen = ₹ 8 From the question, it’s required to find the value of (x + 10y) ⇒ 75 +10(8) = 20 Therefore, the total cost of 1 bag and 10 pens = 75 + 80 = ₹ 155.

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

Answer»

Let the cost of a bag and a pen be ₹ x and ₹ y, respectively.

Then, according to the question

3x + 4y = 257 … (i)

4x + 3y = 324 … (ii)

On multiplying equation (i) by 3 and (ii) by 4,

We get, 9x + 12y = 770 … (iii)

16x + 12y = 1296 … (iv)

Subtracting equation (iii) from (iv), we get

16x – 9x = 1296 – 771

7x = 525

x = 525/7 = 75

Hence, the cost of a bag = ₹ 75

Substituting x = 75 in equation (i), We get,

3 x 75 + 4y = 257

225 + 4y = 257

4y = 257 – 225

4y = 32

y = 32/4 = 8

Hence, the cost of a pen = ₹ 8

From the question, it’s required to find the value of (x + 10y)

⇒ 75 +10(8) = 20

Therefore, the total cost of 1 bag and 10 pens = 75 + 80 = ₹ 155.