Question

The total cost of $8$ books and $5$ pens is $420$ rupees and the total cost of $5$ books and $8$ pens is $321$ rupees. Find the cost of $1$ book and $2$ pens.

Answer 1

Let cost of book be x & cost of pen be y

$\Rightarrow 8x+5y=420;\Rightarrow 5x+8y=321$

Adding = $13x+13y=741;x+y=57$ ____ (1)

Subtracting = $3x-3y=99;x-y=33$

substituting x=y+33 in equation (1) we get :

$y+33+y=57\Rightarrow 2y=24\Rightarrow y=12$

so $x=12+33=45$

cost of 1 book & 2 pens = 45+2(12)= 45+24

$=69Rs$