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
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