Represent the following situation 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.
$A$ 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.
(N/A) Let the number of toys produced on that day be $x$.
Therefore,the cost of production (in rupees) of each toy that day $= 55 - x$.
So,the total cost of production (in rupees) that day $= x(55 - x)$.
Given that the total cost of production is ₹ $750$,we have:
$x(55 - x) = 750$
Expanding the equation:
$55x - x^2 = 750$
Rearranging the terms to form a standard quadratic equation:
$-x^2 + 55x - 750 = 0$
Multiplying by $-1$ to simplify:
$x^2 - 55x + 750 = 0$
Thus,the number of toys produced that day satisfies the quadratic equation $x^2 - 55x + 750 = 0$.
Therefore,the cost of production (in rupees) of each toy that day $= 55 - x$.
So,the total cost of production (in rupees) that day $= x(55 - x)$.
Given that the total cost of production is ₹ $750$,we have:
$x(55 - x) = 750$
Expanding the equation:
$55x - x^2 = 750$
Rearranging the terms to form a standard quadratic equation:
$-x^2 + 55x - 750 = 0$
Multiplying by $-1$ to simplify:
$x^2 - 55x + 750 = 0$
Thus,the number of toys produced that day satisfies the quadratic equation $x^2 - 55x + 750 = 0$.
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