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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.
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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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