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 fo 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 × (55 − x)

∴ x(55 − x) = 750

⇒ 55x – x² = 750

⇒ −x² + 55x – 750 = 0

⇒ x² – 55x + 750 = 0

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

x² – 55x + 750 = 0 which is the required representation of the problem mathematically.

x² – 30x – 25x + 750 = 0

(x – 30)(x – 25) = 0

x = 30 or x = 25