Question

The price of 9 pens and 3 pencil is 99 rupees and the price of 4 pen and 3 pencil is 49 rupees? What is the price of a pen? What is the price of a pencil

Answer 1

Question -

The price of 9 pens and 3 pencils is Rs 99 and the price of 4 pens and 3 pencils is Rs 49. What is the price of a pen? What is the price of a pencil?

Solution -

Let the price of one pen be x and price of one pencil be y

According to the question -

$\implies9x + 3y = 99$

$\implies3y = 99 - 9x.........1)$

And,

$\implies4x + 3y = 49$

$\implies4x + 99 - 9x = 49(by \: 1)$

$\implies - 5x + 99 = 49$

$\implies - 5x = 49 - 99$

$\implies - 5x = - 50$

$\implies x = \frac{ - 50}{ - 5}$

$\implies \: x = 10$

Now putting the value of x in equation 1) we will get -

$\implies3y = 99 - 9x$

$\implies3y = 99 - 9 \times 10$

$\implies3y = 99 - 90$

$\implies3y = 9$

$\implies \: y = \frac{9}{3}$

$\implies \: y = 3$

Therefore the price of one pen is Rs 10 and price of one pencil is Rs 3