Cost of 7 pens and 8 pencils is 87 and cost of 6 pens and 4 pencils is 66. Write linear equation for representing the above data and draw its graph. Also find the cost of 1 pen and 1 pencil from the graph.

Given: Cost of 7 pens and 8 pencils is 87 and cost of 6 pens and 4 pencils is 66.

To find: Here we have to find the cost of 1 pen and 1 pencil from the graph.

Solution:

Let the cost of one pencil be '$x$' and the cost of one pen be '$y$'.

So,

$7y\ +\ 8x\ =\ 87$      .... (i)

And, we have,

$6y\ +\ 4x\ =\ 66$     .... (ii)  

Multiplying equation (ii) by 2 and subtracting equation (i) 

$12y\ +\ 8x\ -\ 7y\ -\ 8x\ =\ 132\ -\ 87$

$5y\ =\ 45$ 

$y\ =\ \frac{45}{5}$

$y\ =\ 9$

Now putting y = 9,

$7(9)\ +\ 8x\ =\ 87$

$63\ +\ 8x\ =\ 87$

$8x\ =\ 87\ -\ 63$

$8x\ =\ 24$

$x\ =\ \frac{24}{8}$

$x\ =\ 3$ 

Hence, Cost of 1 pen = Rs. 9 Cost of 1 pencil = Rs. 3  

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Updated on: 10-Oct-2022

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