Solving Word Problems Involving Quadratic Equations Examples :
In this section, you will learn, how to solve word problems on quadratic equations.
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.
Let 'x' be the number of marbles that john has
Let '45 - x' be the number of marbles that Jivanthi has
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
40 x - x²- 200 + 5 x = 124
45 x - x²- 200 = 124
x²- 45 x + 124 + 200 = 0
x²- 45 x + 324 = 0
x²- 36 x - 9 x + 324 = 0
x (x - 36) - 9 (x - 36) = 0
(x - 9) (x - 36) = 0
x - 9 = 0 x - 36 = 0
x = 9 x = 36
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.
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 = 55 x - x²
x² - 55 x + 750 = 0
x² - 30 x - 25 x + 750 = 0
x (x - 30) - 25 (x - 30) = 0
(x - 30) (x - 25) = 0
x - 30 = 0 x - 25 = 0
x = 30 x = 25
Hence the number of toys produced on that day are 30 or 25.
After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems involving quadratic equations.
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