Let the number of toys produced on that day be ‘x’.
∴ The cost of production (in rupees) of each toy that day = 55 – x
∴ 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.
Now, we have to find out the value of ’x’
x2 – 55x + 750 = 0
x2 – 30x – 25x + 750 = 0
x(x – 30) – 25(x – 30) = 0
(x – 30) (x – 25) = 0
If x – 30 = 0, then x = 30
If x – 25 = 0, then x = 25
∴ x = 30 OR x = 25.