Question

The cost of 4 pens and 4 pencil is ₹100 three times the cost of a pencil box from the pair of linear equation for the above situation find the cost of a pen and a pencil box

Answer 1

Solution :-

Let the cost of a pen be Rs 'x' and the cost of a pencil box be Rs. 'y'

As, the cost of 4 pens and 4 pencil boxes is Rs. 100

So, 4x + 4y = 100 .................(1)

And, three times the cost of a pen is Rs. 15 more than the cost of a pencil box.

So, 3x = y + 15

⇒ 3x - y = 15 ......................(2)

Now multiplying the equation (1) by 3 and equation (2) by 4, we get

⇒ (4x + 4y = 100)*(3) = 12x + 12y = 300 ................(3)

⇒ (3x - y = 15)*(4) = 12x - 4y = 60 ..........................(4)

Now, subtracting (4) from (3)

12x + 12y = 300

12x - 4y = 60

- + -

_________________

16y = 240

_________________

⇒ 16y = 240

⇒ y = 240/16

⇒ y = 15

Now, substituting the value of y = 15 in (2)

⇒ 3x - y = 15

⇒ 3x - 15 = 15

⇒ 3x = 15 + 15

⇒ 3x = 30

⇒ x = 30/3

⇒ x = 10

So, the cost of a pen is Rs. 10 and the cost of a pencil box is Rs. 15

HOPE THIS HELPS!!!