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

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.

Solution:

Given:

(i) Cost of 3 bags and 4 pens = Rs. 257.

(ii) Cost of 4 bags and 3 pens = Rs. 324.

To Find: Cost of 1 bag and 10 pens.

Suppose, the cost of 1 bag = Rs. x.

and the cost 1 pen = Rs. y.

According to the given conditions, we have

3x + 4y = 257,

3x + 4y − 257 = 0 …… (1)

4x + 3y = 324

4x +3y − 324 = 0 …… (2)

Solving equation 1 and 2 by cross multiplication

$\frac{x}{-1296+771}=\frac{-y}{-972+1028}=\frac{1}{9-16}$

$\frac{x}{-525}=\frac{-y}{56}=\frac{1}{-7}$

$x=\frac{-525}{-7}$

$=75$

$\therefore$ cost of 1 bag $=$ Rs. 75 .

cost of l bag $=$ Rs. 75

$y=\frac{-56}{-7}$

$=8$

$\therefore$ cost of 1 pen $=$ Rs. 8

Total cost of 1 bag and 10 pens $=$ Rs. 155

Hence total cost of 1 bag and 10 pens $=$ Rs. 155