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.

Question

Represent the following situations mathematically:

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. We would like to find out how many marbles they had to start with.

Answer 1

Let the number of marbles John had be x.

Then the number of marbles Jivanti had = 45 – x (Why?).

The number of marbles left with John, when he lost 5 marbles = x – 5

The number of marbles left with Jivanti, when she 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 that product = 124)

i.e., – x² + 45x – 324 = 0

i.e., x² – 45x + 324 = 0

Therefore, the number of marbles John had, satisfies the quadratic equation

x² – 45x + 324 = 0

which is the required representation of the problem mathematically.