John and Jivanti together have 45 marbles. Both of them lost 5 marbles each,

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 128. Form the quadratic equation to find how many marbles they had to start with, if John and x marbles.

Solution:

It is given that John had ‘x’ marbles.

We are also given that both John and Javanti had 45 marbles together.
So, Javanti should have ’45 − x’ marbles with her.

Now, it is given that both of them lose 5 marbles each.

So in the new situation, John will have ‘− 5’marbles and Javanti will have ’45 − − 5’ marbles.

Also it is given that the product of the number of marbles both of them now is 128.

Therefore,

$(x-5)(45-x-5)=128$

$(x-5)(40-x)=128$

$40 x-x^{2}-200+5 x=128$

$x^{2}-45 x+200+128=0$

$x^{2}-45 x+328=0$

Hence, this is the required quadratic equation.