Question

Represent the statement in the fomr of a quadratic equation. A cottage industry produces a certain number of toys in a day. The cost of production of each toy is $55$ minus the number of toys produced. On a particular day the total cost of production for the toys produced is $750$.

Answer 1

Step 1: Representing with variables

Let the cost of production of a toy be $x$.

Let the total number of toys produced be $y$.

According tot he question the cost of production of a toy can be represented as,

$x=55-y$

Or,

$y=55-x$

The total cost of production is represented as the product of cost of production of each toy and the number of toys produced.

According to the question, the total cost of production on a particular day can be represented as,

$\left(x\right)\left(y\right)=750$

Step 2: Forming the quadratic equation

Substitute the equation $y=55-x$ into $\left(x\right)\left(y\right)=750$ to form the quadratic equation for the number of toys.

$$\begin{gathered} \left(x\right)\left(55-x\right)=750 \\ \Rightarrow 55x-x^2=750 \\ \Rightarrow x^2-55x+750=0 \end{gathered}$$

Therefore, the quadratic equation that gives the number of marbles is $\begin{array}{rcl}{x}^2-55x+750& =& 0\end{array}$.