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.

Dear Student

Let us say,
the number of marbles John have = x.
Therefore,
number of marble Jivanti have = 45 - x
After losing 5 marbles each,
Number of marbles John have = x - 5
Number of marble Jivanti have = 45 - x - 5 = 40 - x
Given that the product of their marbles is 124.
∴ (x - 5)(40 - x) = 124
⇒ x^2 – 45x + 324 = 0
⇒ x^2 – 36x - 9x + 324 = 0
⇒ x(x - 36) -9(x - 36) = 0
⇒ (x - 36)(x - 9) = 0
Thus, we can say,
x - 36 = 0 or x - 9 = 0
⇒ x = 36 or x = 9
Therefore, If, John's marbles = 36,
Then, Jivanti's marbles = 45 - 36 = 9
And if John's marbles = 9,
Then, Jivanti's marbles = 45 - 9 = 36

Thanks