John and Jivani 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 had $x$ marbles.
Given:
John and Jivani together have $45$ marbles.
Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $128$.
To do:
Here, we have to form the quadratic equation to find the number of marbles they had to start with, if John had $x$ marbles.
Solution:
Number of marbles with John $=x$
Number of marbles with Jivani $=45-x$
Number of marbles John had after losing 5 marbles $= x - 5$
Number of marbles Jivani had after losing 5 marbles $= (45 - x) - 5 = 40 - x$
The product of the marbles they now have $=128$.
Therefore,
$(x - 5)(40 - x) = 128$
$40x-x^2-200+5x = 128$
$x^2 - 45x + 128 + 200 = 0$
$x^2 - 45x + 328 = 0$
The required quadratic equation is $x^2-45x+328=0$.
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