Solve the problems given in Example 1.
(i) Let the number of John’s marbles be x.
Therefore, number of Jivanti’s marble = 45 − x
After losing 5 marbles,
Number of John’s marbles = x − 5
Number of Jivanti’s marbles = 45 − x − 5 = 40 − x
Given that the product of their marbles is 124.
∴ (x – 5) (40 – x) = 124
= x2 – 45x +324 = 0
= x2 – 36x – 9x +324 = 0
= x(x – 36 ) – 9 (x – 36 ) = 0
= (x – 36) (x – 9) = 0
Either x – 36 = 0 or x − 9 = 0
i.e.,
x = 36 or x = 9
If the number of John’s marbles = 36,
Then, number of Jivanti’s marbles = 45 − 36 = 9
If number of John’s marbles = 9,
Then, number of Jivanti’s marbles = 45 − 9 = 36
(ii) Let the number of toys produced be x.
∴ Cost of production of each toy = Rs (55 − x)
It is given that, total production of the toys = Rs 750
∴ x(55 – x) = 750
= x2 – 55x+750 = 0
= x2 – 25x – 30x+750 = 0
= x(x – 25 ) – 30(x – 25 ) = 0
= (x – 25)(x – 30) = 0
Either x – 25 = 0 or x − 30 = 0
i.e., x = 25 or x = 30
Hence, the number of toys will be either 25 or 30.