## Quadratic Equation Solution14

In this page quadratic equation solution14 we are going to see solution of the word problems of the topic quadratic equation.

Question 21

1 year ago a father was 8 times as old as his son. Now his age is square of his son’s age. Find the present age.

Solution:

Here the age of father is compared by his son age.

So “x” his father’s preset age

Let “y” be his son’s age

One year ago his father’s age = x – 1

(x - 1) =  8 (y – 1) ----- (1)

x = y²  ------ (2)

now we are going to apply the value of x in the first equation

x – 1 = 8 y – 8

y²  - 8 y – 1 + 8 = 0

y²  - 8 y + 7 = 0

y²  - 7 y – 1 y + 7 = 0

y (y – 7) – 1 (y - 7) = 0

(y - 1) (y – 7) = 0

y – 1 = 0                 y - 7 =0

y = 1                         y = 7

Here y represents the present age of son.

Now we are going to apply the values of y in the second equation to get the value of x

If  y = 1

x = (1)²

x = 1

If  y = 7

x = (7)²

x = 49

Therefore the present age of father = 49 years

Present age of son = 7 years

Verification:

1 year ago a father was 8 times as old as his son

49 – 1 = 8 (7 – 1)

48 = 8 (6)

48 = 48

Now his age is square of his son’s age.

49 = 72

49 = 49 