# WORD PROBLEMS ON QUADRATIC EQUATIONS WITH SOLUTIONS

Word Problems on Quadratic Equations with Solutions :

In this section, you will learn how to solve word problems on quadratic equations.

## Solving Word Problems Involving Quadratic Equations Examples

Example 1 :

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 \$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  =  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

Example 2 :

Find two numbers whose sum is 27 and product is 182.

Solution :

Let 'x' and '27 - x' are two numbers

Sum of those numbers  =  27

product of those numbers  =  182

x (27 - x)  =  182

27 x - x²  =  182

x² - 27 x + 182  =  0

x² - 14 x - 13 x + 182  =  0

x (x - 14) - 13 (x - 14)  =  0

(x - 14) (x - 13)  =  0

x - 14  =  0          x - 13  =  0

x  =  14                x  =  13

Example 3 :

Find two consecutive positive integers, sum of whose squares is 365.

Solution :

Let 'x' and 'x + 1' are two consecutive integers

sum of whose squares  =  365

x² + (x + 1)²  =  365

x² + x²+ 2 x + 1  =  365

x² + 2 x + 1 - 365  =  0

x² + 2 x - 364  =  0

÷ by 2 = > x² + x - 182  =  0

x² + 13 x - 12 x - 182  =  0

x (x + 13) - 12(x + 13)  =  0

(x - 12) (x + 13)  =  0

x - 12  =  0      x + 13  =  0

x  =  12           x  =  -13

Since it is positive integer, -13 is not admissible.

x  =  12

x + 1  =  13

Therefore the two consecutive integers are 12 and 13.

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems on quadratic.

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