Question

Two years ago my age was 9/2 times the age of son. 6 years ago, my age
was twice the square of the age of my son. What is the present age
of me and my son.
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Answer 1

Let son's present age be 'x'.

Two yrs ago:

Son's age =x-2

My age =9/2(x-2)=4.5x -9

Six years ago:

Son's age= x-6

My age=2×(x-6)^2=2x^2-24x+72

4.5x-9-4 = 2x^2-24x +72

2x^2-28.5x+85=0

(4x-17)(x-10)=0

#4x-17=0::x=17/4

#x-10=0::x=10(possible)

Hence,present age of son =10yrs

present age of me=38yrs.....

Answer 2

Answer:

• My son's age = 22 years

• My age = 92 years

Given:

• Two years ago my age was 9/2 times the age of son.

• 6 years ago, my age was twice the square of the age of my son.

To find :

• What is the present age of me and my son =?

Step-by-step explanation:

Let the present age of my son be x

Then, my age be y.

And, 2 years ago my sons age = x - 2

So,2 years ago me's age = y - 2

Ist A. T. Q ⟹

9/2(x-2) = y - 2

9x - 18/2 = y - 2

9x - 18 = 2y - 4

9x - 2y = 18 - 4

9x - 2y = 14 ..... (i)

Now,

6 years ago age of both,

x - 6x and y - 6.

2nd A. T. Q. ⟹

x - 6 = y - 6

4 ( x - 6 ) = y - 6

4x - 24 = y - 6

4x - y = 24 - 6

4x - y = 18. ..... (ii)

Multiply equation (ii)by 2

2(4x - y = 18)

8x - 2y = 36

Combining both equations, we get

- x = 22

Negative term is not variable.

So, x = 22 years.

Putting 22 in equation (i), we get

9x - 2y = 14

9 × 22 - 2y = 14

198 - 2y = 14

- 2y = 14 - 198

- 2y = 14 - 198

- 2y = - 184

y = - 184/-2

y = 92

Hence, My son age = 22 years

My age = 92 years.