Question

The cost of 4 pens and 4 pencil box is Rs 100.Three times the cost of a pen is rupees 15 more than the cost of a pencil box. Form a pair of linear equation for the above situation find the cost of pen and pencil box

Answer 1

Answer:

Step-by-step explanation:

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

Answer.

Answer 2

Answer:

Step-by-step explanation:

Let no. of pens = X

pencil box=Y

4X+4Y=100

THEREFORE X+Y= 25--------(1)

IN EQN(2)

3X=Y+15

THEREFORE; 3X-Y=15----------(2)

ADDING (1) AND (2)

4X=40

X=10

THEREFORE Y=5