Question

Represent the following situation mathematically:
Raju and Rajendar together have 45 marbles. Both of them lost 5 marbles each, and
the product of the number of marbles now they have is 124. We would like to find out
how many marbles they had previously.

Answer 1

Answer:  

x² - 45x + 324 = 0

Step-by-step explanation:

Let the number of marbles

Raju had be x .

Then the number of marbles

Rajendar had = 45 - x

[ Since , Total marbles = 45 ]

The number of marbles left with

Raju , when he lost 5 marbles

= x - 5

The number of marbles left with

Rajendar , 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 ]

=> -x² + 45x - 324 = 0

=> x² - 45x + 324 = 0

Therefore ,

the number of marbles Raju

had ' x ' , satisfies the Quadratic

Equation x² - 45x + 324 = 0

Which is the required

representing of the problem

mathematically .