Question

Represent the following situations mathematically:

(i) John and Jivanti together have $45$marbles. Both of them lost $5$marbles each, and the product of the number of marbles they now have is$124$. We would like to find out how many marbles they had to start with.

(ii) 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 `$750$. We would like to find out the number of toys produced on that day.

Answer 1

(i) We will assume, the number of marbles John have $=x$

Hence, the number of marble Jivanti have$=45–x$

After losing $5$ marbles each,

Number of marbles John has$=x–5$

Number of marble Jivanti have $=45–x–5=40–x$

Given that the product of their marbles is$124$

$$\begin{gathered} \therefore (x–5)(40–x)=124 \\ \Rightarrow x^2–45x+324=0 \\ \Rightarrow x^2–36x–9x+324=0 \\ \Rightarrow x(x–36)-9(x–36)=0 \\ \Rightarrow (x–36)(x–9)=0 \end{gathered}$$,

we can consider,

$$\begin{gathered} x–36=0orx–9=0 \\ \mathbf{}\mathbf{\Rightarrow }\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{36}\mathbf{}\mathit{o}\mathit{r}\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9} \end{gathered}$$

Thus,

If

The number of marbles John have $\mathit{x}\mathbf{=}\mathbf{9}$

The number of marble Jivanti has $=45-x=45-9\mathbf{=}\mathbf{36}$

If

The number of marbles John have $\mathit{x}\mathbf{=}\mathbf{36}$

The number of marble Jivanti has $=45-x=45-36\mathbf{=}\mathbf{9}$