Question

5 pencils &7 pens together cost Rs.50 whereas 7 pencils & 5 pens together costs Rs. 45
.find the cost of one pen & one pencil

Answer 1

ANSWER:-

Given:

5 pencil & 7 pens together cost Rs.50. whereas 7 pencil & 5 pens together costs Rs.45.

To find:

Find the cost of one pen & one pencil.

Solution:

Let the cost of 1 pencil be Rs.x & the cost of 1 pen be Rs.y

According to the question:

Here, equation;

⚫5x + 7y = 50............(1)

⚫7x + 5y = 45............(2)

From equation (1), we get;

=) 5x +7y = 50

=) 5x= 50 -7y

=) x= 50-7y/5........(3)

Eliminate the value of x in equation (2), we get;

$= > 7x + 5y = 45 \\ \\ = > 7( \frac{50 - 7y}{5} ) + 5y = 45 \\ \\ = > \frac{350 - 49y}{5} + 5y = 45 \\ \\ = > 350 - 49y + 25y = 225 \\ \\ = > 350 - 24y = 225 \\ \\ = > - 24y = 225 - 350 \\ \\ = > - 24y = - 125 \\ \\ = > y = \frac{ - 125}{ - 24} \\ \\ = > y = Rs.5.2$

Now,

Putting the value of y in equation (3),we get;

$= > x = \frac{50 - 7y}{5} \\ \\ = > x = \frac{50 - 7(5.2)}{5} \\ \\ = > x = \frac{50 - 36.4}{5} \\ \\ = > x = \frac{13.6}{5} \\ \\ = > x =Rs.2.72$

Thus,

Cost of one pencil is, x= Rs.2.72

=) Rs.3 [approx]

&

Cost of 1 pen is, y= Rs.5.2

Hope it helps ☺️