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 $124$. From the quadratic equation to find how many marbles they had to start with, if John had $x$ marbles.

• A. $36,9$
• B. $20,25$
• C. $30,15$
• D. $27,18$

Answer 1

The correct option is A $36,9$

Given John and Jivanti together have $45$ marbles

Let the number of Marbles John had be $=x$

Then the number of marbles Jivanti had$=45-x$

Both of them lost $5$ Marbles each

Therefore, the number of marbles John had$=x-5$

The number of marbles Jivanti had$=45-x-5=40-x$

Now product of the number of Marbles $=124$

$\therefore (x-5)(40-x)=124$

$40x-x²-200+5x=124$

$-x²+45x-200-124=0$

$x²-45x+328=0$ --- (Multiplying by(-1))

By factorization method

$x^2-36x-9x+324=0$

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

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

$x=36$ or $x=9$

When John has $36$ Marbles, Jivanti has $=45-x=45-36=9$ marbles

When John has $9$ Marbles and Jivanti has $=45-x=45-9=36$ marbles