Question

The price of a pen is 9 rupees more than the price of a pencil. the price of a book is 8 rupees more than the price of a pen.total price of 12 pens and 12 pencils is equal to the total price of 9 books .find price of a pencil,pen and a book

Answer 1

Define x:

Let the price of a pencil be x

⇒ Pencil  = x

The price of a pen is 9 rupees more than the price of a pencil

⇒ Pen = x + 9

The price of the book is 8 rupees more than the price of a pen

⇒ Book = (x + 9) + 8

⇒ Book = x + 17

Solve x:

12 pens and 12 pencils is equal to the total price of 9 books

12 (x + 9) + 12x = 9(x + 17)

Distribute 12 and 9:

12x + 108 + 12x = 9x + 153

Combine like terms:

24x + 108 = 9x + 153

Take away 108 from both sides:

24x = 9x  + 45

Take away 45 from both sides:

15x = 45

Divide both sides by 15:

x = 3

Find the price of the items:

Pencil = x = 3 rupees

Pen = x + 9 = 3 + 9 = 12 rupees

Book = x + 17 = 3 + 17 = 20 rupees

Answer: Pencil = 3 rupees, Pen = 12 rupees and Book = 20 rupees

Answer 2

Let the price of a pencil be ₹ x.

So,
price of the pen = ₹ (x+9) [ The price of pen is 9 rupees more than the price of a pencil ]

price of book = ₹ [ (x+9) + 8 ] = ₹ (x + 17) [ The price of book is 8 rupees more than the price of a pen ]

According to the question,
$\bf{Total \:price \:of \:12 \:pens\: and\: 12\: pencils\: is \:equal \:to \:the\: total \:price\: of\: 9 \:books. }$

Price of 12 pens = 12 × ₹ x = ₹ 12x

Price of 12 pencils = 12 × ₹ (x+9) = ₹ (12x + 108)

Price of 9 books = 9 × ₹ (x+17) = ₹ (9x + 153)

=> 12x + (12x + 108) = 9x + 153

=> 24x + 108 = 9x + 153

=> 24x - 9x = 153 - 108

=> 15x = 45

=> x = 45/15

=> x = 3

Hence,
Price of a pencil = ₹ x = ₹ 3

Price of a pen = ₹ (x+9) = ₹ 12

Price of a book = ₹ (x + 17) = ₹ 20