Question

Solve the problems given in Example 1:-

(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. Find out how many marbles they had to start with.

(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 Rs 750. Find out the number of toys produced on that day.

Answer 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 

It is given that the product of their marbles is 124. 
∴ (x-5) (40-x) =124
⇒ \(x^2 -45x +324 = 0\)
⇒ \(x^2 -36 x -9x +324 =0\)
⇒ \(x(x-36)-9(x-36) =0\)
⇒ \((x-36) (x-9)=0\)

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
and
If number of John’s marbles = 9,
Then, number of Jivanti’s marbles = 45 − 9 = 36

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(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
⇒ \(x^2 -55x +750 =0\)
⇒ \(x^2 -55x +750 =0\)
⇒ \(x^2- 25x -30x +750 =0\)
⇒ \(x(x-25) -30(x-25) =0\)

 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.