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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.
Solution
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
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