CHAPTER-4 QUADRATIC EQUATIONS
QUESTION -2
Solve the problems given in Example 1
SOLUTION:
The problem in example 1 was as follows: Represent the following situations mathematically: (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 ₹ 750. We would like to find out the number of toys produced on that day.
Given: (i) Let the number of marbles that John had be x. The number of marbles Jivanti had will be = 45 – x Both of them lost 5 marbles each: Marbles with John = x – 5 Marbles with Jivanti = 45 – x – 5 = 40 – x Product of current number of marbles = 124 Let us use this condition to form a
On multiplying both sides of the equation with negative sign, we get
John and Jivanti started with 36 and 9 marbles.
(ii) Let the number of toys produced in a day be x.
Cost of each toy = (55 – x) rupees
Total cost of production = cost of each toy × Total number of toys
The number of toys produced on that day is 25 or 30.