Question

A man purchased some pens at Rs 8 each and some pencils at 2.5Rs each. If the total numbers of pens and pencils is 27 and their total cost is 150Rs. How many pens did he buy?

Answer 1

Let number of pens = 'x' and number of pencils = 'y'
given x + y =27 and 8x + 2.5y = 150
on solving x = 15 and y = 12

Answer 2

Given,

A man purchased some pens at Rs 8 each and some pencils at 2.5Rs each.

Total number of pens and pencils purchased = 27

The total cost of all the pens and pencils = Rs. 150

To find,

The number of pens purchased.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the number of pens purchased by the man is x and the number of pencils purchased is y, respectively.

Now, according to the question;

Total number of pens and pencils purchased = 27

=> number of pens purchased + the number of pencils purchased = 27

=> x + y = 27

=> x = (27 - y)

{Equation-1}

Also, according to the question;

The cost of each pen purchased = Rs. 8

So, the total cost of x pens purchased by the man = (number of pens purchased) × (cost of each pen)

= Rs. 8x

And, the cost of each pencil purchased = Rs. 2.5

So, the total cost of y pencils purchased by the man = (number of pencils purchased) × (cost of each pencil)

= Rs. 2.5y

Now, according to the question;

The total cost of all the pens and pencils = Rs. 150

=> (the total cost of x pens purchased by the man) + (the total cost of y pencils purchased by the man) = Rs. 150

=> Rs. 8x + Rs. 2.5y = Rs. 150

=> 8x + 2.5y = 150

=> 8(27-y) + 2.5y = 150

{according to equation-1}

=> 216 - 8y + 2.5y = 150

{By further solving the equation}

=> 8y - 2.5y = 216 - 150

=> 5.5y = 66

=> y = 66/5.5 = 660/55 = 60/5 = 12

=> y = 12

=> number of pencils purchased = 12

Now, substituting the value of y in equation-1, we get;

x = (27 - y) = 27-12 = 15

=> x = 15

=> number of pens purchased = 15

Hence, the man purchased 15 pens.