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 articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, form the quadratic equation of find x.

Answer 1

As per question, the number of toys produced on that day be x.

∴ The cost of production (in rupees) of each toy on that day = 55–x

So, the total cost of production (in rupees) that day = x$\times$(55−x)

∴ x(55−x)=750

⇒ $55x–x^2=750$

⇒ $-x^2+55x–750=0$

⇒ $x^2–55x+750=0$

∴ The number of toys produced that day satisfies the quadratic equation.

$x^2–55x+750=0$ which is the required representation of the problem mathematically.