Q3 of 168 Page 7

Represent the following situations mathematically:

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.

Let ‘x’ be the number of marbles John had.

∴ Jivanti will have 45 − x marbles.


[∵ the total number of marbles is 45]


As both of them lost 5 marbles each; marbles they now have will be x − 5 and 40 − x respectively.


⇒ Product of the number of marbles = (x − 5) (40 − x)


∴ 40x − x2 − 200 + 5x = 124 [∵ the product is 124]


⇒ x2 − 45x + 324 = 0


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