A Cottage Industry Produces Toys – Form the Quadratic Equation
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 ₹750. If \(x\) denotes the number of toys produced that day, form the quadratic equation to find \(x\).
Solution
Let the number of toys produced in a day be
\[ x \]
Cost of production of each toy
\[ = 55 – x \]
Total cost of production
\[ = \text{Number of toys} \times \text{Cost per toy} \]
\[ x(55-x)=750 \]
Expanding,
\[ 55x-x^2=750 \]
Bringing all terms to one side,
\[ x^2-55x+750=0 \]
Required Quadratic Equation
\[ \boxed{x^2-55x+750=0} \]
Answer
If \(x\) denotes the number of toys produced on that day, then the required quadratic equation is
\[ \boxed{x^2-55x+750=0} \]
This equation can be solved to find the number of toys produced.