Question

John and jivanti together 45 Marbles both of them lost 5 Marbles each and the product of the number of marble they have is 124 find the find out how many Marbles they had to start with.

Answer 1

Let the no. of marbles john had be x
Then the no. of marbles jivanti had = (45-x)
The no. of marbles left with john, when he lost 5 marbles = 45-x-5=40 - x
Therefore their product = (x-5)(40-x)
=40x - x2 -200+5x
=x2+45x-200
So,-x2 + 45x-200=124. (given , product =124)
so, x2-45x+324=0
Therefore, the no. of marbles john had , satisfies the quadratic eqn ,
x2-45x+324.


When u will find the value x of this eqn that no. will be the no. of marbles they started with!


Hope it helps

Answer 2

Let the number of john's marbles be x.

Therefore, number of jivanti's marble = 45 - x

After losing 5 marble,

Number of john's marbles = x - 5

Number of jivanti's marbles = 45 - x - 5 = 40 - x

The product of the number of marbles is 124.

Therefore,

=> (x - 5) (40 - x) = 124

=> 40x - x² - 200 + 5x = 124

=> x² - 45x + 200 = - 124

=> x² - 45x + 324 = 0

=> x² - 36x - 9x + 324 = 0

=> x(x - 36) - 9(x - 36) = 0

=> (x - 36) (x -9)

=> x - 36 = 0 or x - 9 = 0

=> x = 36 or x = 9

The number of john's marbles = 36

Thus, the number of jivanti's marbles = 45 - 36 = 9

Number of john's marbles = 9

Thus, number of jivanti's marbles = 45 - 9 = 36.