John and jivanthi 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.
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Answers
Step-by-step explanation:
Let the number of marbles John had be 'x'.
Given that together they have 45 marbles.
So,the number of marbles jivanthi have be '45 - x'.
Now,
Given that both of them lost 5 marbles each.
Number of marbles with John = x - 5.
Number of marbles with jivanthi = 45 - x - 5 = 40 - x.
Given that product of number of marbles they have is 124.
⇒ (x - 5)(40 - x) = 124
⇒ 40x - x² - 200 + 5x = 124
⇒ -x² + 45x - 324 = 0
⇒ x² - 45x + 324 = 0
⇒ x² - 36x - 9x + 324 = 0
⇒ x(x - 36) - 9(x - 36) = 0
⇒ (x - 9)(x - 36) = 0
⇒ x = 9, 36
When x = 9:
Then, 45 - 9 = 36.
When x = 36:
Then, 45 - 36 = 9.
Therefore:
(i) If, Number of marbles with john = 9 then, number of marbles of jivanthi = 36.
(ii) If, number of marbles with john = 36, then, number of marbles with jivanthi = 9.
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