A cottage industry produces a certain number | vedclass

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Question

(A) Let the number of toys produced in a day be $x$.The cost of production of each toy (in rupees) is $(55 - x)$.The total cost of production is given

Vedclass · Accepted Answer

$25$ or $30$

Vedclass · Answer

(A) Let the number of toys produced in a day be $x$.The cost of production of each toy (in rupees) is $(55 - x)$.The total cost of production is given by the product of the number of toys and the cost per toy:$x(55 - x) = 750$Expanding the equation:$55x - x^2 = 750$Rearranging into the standard quadratic form $ax^2 + bx + c = 0$:$x^2 - 55x + 750 = 0$To solve this,we factorize the quadratic equation by splitting the middle term:$x^2 - 25x - 30x + 750 = 0$Grouping the terms:$x(x - 25) - 30(x - 25) = 0$$(x - 25)(x - 30) = 0$Setting each factor to zero:$x - 25 = 0 \Rightarrow x = 25$$x - 30 = 0 \Rightarrow x = 30$Therefore,the number of toys produced on that day was either $25$ or $30$.

$A$ 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 $Rs$ $750$. Find out the number of toys produced on that day.

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