# A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.

Given:

A cottage industry produces a certain number of pottery articles in a day.

On a particular day, the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day.

Total cost of production on that day $=Rs. 90$.

To do:

Here, we have to find the number of articles produced and the cost of each article.

Solution:

Let the number of articles produced be $x$.

This implies,

Cost of production of each article $=Rs. 2x+3$.

The total cost of production is the product of the number of articles produced in a day and the cost of production of each article $=Rs. x(2x+3)$.

According to the question,

$x(2x+3) = 90$

$2x^2+3x = 90$

$2x^2+3x-90 = 0$

Solving for $x$ by factorization method, we get,

$2x^2+15x-12x-90=0$

$2x(x-6)+15(x-6)=0$

$(x-6)(2x+15)=0$

$x-6=0$ or $2x+15=0$

$x=6$ or $2x=-15$

Therefore, the value of $x$ is $6$.   ($x$ cannot be negative)

$2x+3=2(6)+3=12+3=15$

The number of articles produced is $6$ and the cost of each article is $Rs. 15$.