Question

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of particles produced in a day. On a particular day, the cost of production was $750$. If $x$ denotes the number of toys produced that day, find the quadratic equation to find $x$.

Answer 1

Hint: To find out the quadratic equation, we need to solve the question part by part.
We need to consider that the number of toys produced every day must be $x$.
Finally we get the required answer.

Complete step-by-step answer:
It is stated in the question that the cost of production of each toy is found to be $55$ minus the number of particles in a day.
So, we can write that the cost of production of each toy is equal to $55 - x$
Since it is given in the question that the number of toys produced on that day $x$.
Now, cost of production is multiplied by the number of toys,
So we can write it as,
$ = x(55 - x)$
Also, it is given that the cost of production on a particular day $ = 750$
So we can write it as,
$x(55 - x) = 750$
Now, we have to do multiplication we get-
$55x - x_{}^2$$ = 750$
By moving $750$ on the left hand side we get-
$55x - x_{}^2 - 750 = 0$
Now taking ($ - $) as common we get-
$x_{}^2 - 55x + 750 = 0$
Thus the required quadratic equation is $x_{}^2 - 55x + 750 = 0$

Note: It is a simple question which can be solved by applying algebra techniques but for solving this question you need to read the question very carefully otherwise you will surely make mistakes.
So try to keep your focus on it and find the ultimate equation that is the required quadratic equation.