Q2: (a) 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.

Q2: (a) 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.

Solution 

Let the number of marbles of  John = x

Given that John and Jivanti together have 45 marbles

So that number of marbles of Jivanti = 45 – x

Given that Both of them lost 5 marbles each

The number of marbles of  John = x – 5

The number of marbles of  Jivanti= 45 – x – 5 = 40 – x

Given that product of the number of marbles they now have is 124

So that

(x – 5) (40 – x) = 124 

Multiply the values we get  

    40x – x² – 200 + 5x = 124

simplify it

    – x² + 45x – 200 – 124 = 0

simplify it more

    – x² + 45x – 324 = 0

or   x² – 45x + 324 = 0

 If the number of marbles of John  = 36, then, number of marbles of Jivanti = 45 − 36 = 9

If the number of marbles of John  = 9, then, number of marbles of Jivanti = 45 − 9 = 36