Question

The cost of 4 pens and 4 pencil boxes is rs100. Three times the coat of a pen is rs 15 more than the cost of pencil box. Form the paid of linear equations for the above situation. Find the cost of a pen and pencil box

Answer 1

Answer:

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 

 -      +         -

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         16y = 240

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⇒ 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.

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