Question

Question 2(i)
(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. Find out how many marbles they had to start with.

Answer 1

(i) Let the number of John's marbles be $x$.
Therefore, number of Jivanti's marble = $45-x$
After losing 5 marbles,
Number of John's marbles = $x-5$
Number of Jivanti's marbles = $45-x-5=40-x$
It is given that the product of their marbles is $124$.
$\therefore (x-5)(40-x)=124$
$\Rightarrow x^2-45x+324=0$
$\Rightarrow x^2-36x-9x+324=0$

(Splitting the middle term -45x as -36x-9x because $-36x\times -9x=324x^2$)


$\Rightarrow x(x-36)-9(x-36)=0$
$\Rightarrow (x-36)(x-9)=0$
Either $x-36=0orx-9=0$
$\Rightarrow x=36orx=9$
If the number of John's marbles = $36$,
Then, number of Jivanti's marbles = $45-36=9$
If number of John's marbles = $9$,
Then, number of Jivanti's marbles = $45-9=36$