3. 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 to find x.

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Explain, how did we split the number in the equation.

Solution:Given that x denotes the number of toys produced in a day.

So, the cost of production of each toy = (55 – x)

And the total cost of production is the product of the number of toys produced in a day and the cost of production of each toy, i.e., x (55 – x)

From the question, it’s given that

The total cost of production on that particular day is Rs.750.

So,

⇒ x (55 – x) = 750

⇒ 55x – x

^{2}= 750⇒ x

^{2 }– 55x + 750 = 0Thus, the required quadratic equation is x^{2 }– 55x + 750 = 0