Afather’s age is the square of his son’s age (x). in 20 years’ time the father will be 3 times as old as his son. what are the ages of the father and son?

i am supposed to solve this by writing and solving a quadratic equation but i don't know how. the ages are 64 and 8.

Present age of the father is 64 years and age of the son is 8 years.

Let the present age of father = y years

And the present age of son = x years

Now first statement states, "father's age is the square of his son's age".

Equation by this statement will be,

y = x² (1)

Second statement states, "After 20 years, father will be 3 times as old as his son"

So the equation will be,

(y + 20) = 3(x + 20)

y + 20 = 3x + 60

y = 3x + 60 - 20

y = 3x + 40 (2)

By substituting the value of y in equation (2) from equation (1),

x² = 3x + 40

x² - 3x - 40 = 0

x² - 8x + 5x - 40 = 0

x(x - 8) + 5(x - 8) = 0

(x + 5)(x - 8) = 0

x = -5, 8

But age can't be negative.

Therefore, x = 8 years

By substituting the value of x in equation (1),

y = 8²

y = 64 years

         Therefore, present age of the father is 64 years and age of the son is 8 years.

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