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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
⇒ x2 – 45x + 324 = 0
⇒ x2 – 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
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