Question

A cottage industry produces a certain amount of pottery articles in a day. it was observed on a particular day that the cost of production of each article was $3$ more than twice the no. of articles produced on that day. if the total cost of production was $Rs.90$ find the no. of articles produced and the cost of each article.

Answer 1

Let n be no of articles produced that day.

cost of production of each article $=2n+3$

Total cost of production $=n(2n+3)=90$

$\therefore 2n^2+3n=90$

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

We have a formula for solving quadratic equation $a{x}^2+bx+c=0$ is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\therefore n=\frac{-3\pm \sqrt{9+4\times 2\times 90}}{2\times 2}=\frac{-3\pm \sqrt{9+720}}{4}$

$n=\frac{-3\pm \sqrt{729}}{4}=\frac{-3\pm 27}{4}=\frac{-30}{4}$ or $6$

Since n needs to be integer, $n=6$ & cost of production = $2n+3=15$