Represent the following situations mathematically:

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 toys produced in a day. On a particular day, the total cost of production was ` 750. We would like to find out the number of toys produced on that day.

Dear student

Let us say, number of toys produced in a day be x.
Therefore, cost of production of each toy = Rs(55 - x)
Given, total cost of production of the toys = Rs 750
∴ x(55 - x) = 750

x^2 – 55x + 750 = 0
⇒ x^2 – 25x - 30x + 750 = 0
⇒ x(x - 25) -30(x - 25) = 0
⇒ (x - 25)(x - 30) = 0
Thus, either x -25 = 0 or x - 30 = 0
⇒ x = 25 or x = 30
Hence, the number of toys produced in a day, will be either 25 or 30.

Thanks