#### Question

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

#### Solution

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.

∴ (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

Either x - 36 = 0 or x - 9 = 0

⇒ x = 36 or x = 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