Quadratic Equation Solution15





In this page quadratic equation solution15 we are going to see solution of the word problems of the topic quadratic equation.

Question 22

The sum of the age of a father and his son is 45 years. Five years ago the product of their ages was 124. Determine their present age.

Solution:

Let “x” be the present age of father

Let “y” be the present age of son

The sum of the age of a father and his son is 45 years

x + y = 45

y = 45 – x  ------(1)

Five years ago his father’s age = x - 5  

Five years ago son’s age = y – 5

Five years ago the product of their ages was 124.

(x – 5) (y – 5) = 124

(x – 5) (45 – x – 5) = 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

Here x represent the present age of father. So x = 9 is not possible.

x = 36 is possible

To find the value of y we are going to apply the value of x in the second equation.

y = 45 – x

y = 45 - 36

y = 9

Therefore the present age of father = 36 years

Present age of son = 9 years

Verification:

The sum of the age of a father and his son is 45 years.

x + y = 45

36 + 9 = 45

45 = 45

Five years ago the product of their ages was 124

(36 - 5) (9 - 5) = 124

31 (4) = 124

124 = 124

quadratic equation solution15 quadratic equation solution15