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Question

Solve:
(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.
(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. We would like to find out the number of toys produced on that day.

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Solution

(i) Let John have x marbles, so Jayanti will have (45x) marbles.
After losing 5 marbles,
John will have (x5) marbles
Jivanti will have (45x5)=(40x) marbles
As per the given condition,
(x5)(40x)=124
(x5)(x40)=124
x2+45x200=124
x245x+324=0
x236x9x324=0
x(x36)9(x36)=0
(x36)(x9)=0
x36=0 or x9=0
x=36 or x=9

So, if John has 36 marbles, Jivanti will have 9 marbles.
If John has 9 marbles, Jivanti will have 36 marbles.


(ii) Let the total number of toys produced in a day be x.
Cost of production of one toy =Rs.(55x)
x(55x)=750
x255x+750=0
x225x30x+750=0
x(x25)30(x25)=0
(x25)(x30)=0
x25=0 or x30=0
x=25 or x=30

So, total number of toys produced in a day are 25 or 30.

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