# SOLVING WORD PROBLEMS INVOLVING QUADRATIC EQUATIONS EXAMPLES

Example 1 :

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they have now is 124. We would like to find out how many marbles they had to start with.

Solution :

Let 'x' be the number of marbles that john has.

Then, the number of marbles that Jivanthi has '45 - x'.

After losing 5 marbles,

number of marbles with John  =  x - 5

number of marbles with Jivanti  =  45 - x - 5  =  40 - x

The product of number of marbles  =  124

(x - 5)(40 - x)  =  124

40x - x- 200 + 5x  =  124

45x - x- 200  =  124

x- 45x + 124 + 200  =  0

x- 45x + 324  =  0

x2- 36x - 9x + 324  =  0

x(x - 36) - 9(x - 36)  =  0

(x - 9)(x - 36)  =  0

x - 9  =  0  or  x - 36 = 0

x  =  9  or  x  =  36

If x  =  9,

45 - x  =  45 - 9  =  36

If x  =  36,

45 - x  =  45 - 36  =  9

So, John is having 36 marbles, when Jivanti is having 9 marbles or Jivanti is having 36 marbles, when John is having 9 marbles.

Example 2 :

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, the total cost of production was Rs. 750. We would like to find the number of toys produced on that day.

Solution :

Let 'x' be the number of toys produced in a particular day

cost of production of one toy = 55 - x

Total cost  =  Number of toys produced on that day x cost of one toy

Total cost  =  x (55 - x)

750  =  55x - x2

x2 - 55x + 750  =  0

x2 - 30x - 25x + 750  =  0

x(x - 30) - 25(x - 30)  =  0

(x - 30)(x - 25)  =  0

x - 30  =  0  or  x - 25  =  0

x  =  30  or  x  =  25

So, the number of toys produced on that particular day is 30 or 25.

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