Question -
Answer -
(i) John and Jivantitogether have 45 marbles. Both of them lost 5 marbles each, and the product ofthe number of marbles they now have is 124. We would like to find out how manymarbles they had to start with.
(ii) A cottageindustry produces a certain number of toys in a day. The cost of production ofeach toy (in rupees) was found to be 55 minus the number of toys produced in aday. On a particular day, the total cost of production was ` 750. We would liketo find out the number of toys produced on that day.
Solutions:
(i) 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.
Soiution
(i) Let us say, the number of marbles Johnhave = x.
Therefore, number of marble Jivanti have = 45– x
After losing 5 marbles each,
Number of marbles John have = x –5
Number of marble Jivanti have = 45 – x –5 = 40 – x
Given that the product of their marbles is124.
∴ (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
Thus, we can say,
x – 36 = 0or x – 9 = 0
⇒ x = 36 or x = 9
Therefore,
If, John’s marbles = 36,
Then, Jivanti’s marbles = 45 – 36 = 9
And if John’s marbles = 9,
Then, Jivanti’s marbles = 45 – 9 = 36
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ` 750. We would like to find out the number of toys produced on that day.
Solution
(ii) Let us say, number of toys produced in aday be x.
Therefore, cost of production of each toy =Rs(55 – x)
Given, total cost of 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
Thus, either x -25 = 0or x – 30 = 0
⇒ x = 25 or x = 30
Hence, the number of toys produced in a day,will be either 25 or 30.