Quadratic word problem (1 Viewer)

AstroNerd · Nov 3, 2015

Hey guys, I'm not quite sure how u would solve this so if anyone could help that would be great!

a fathers age is the square of his sons 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?

Thanks

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nerdasdasd · Nov 3, 2015

The first sentence is there to trick you.

Let son = x +20
father = 3 * (x + 20)^2 .

Do the algebra/equating and the answer should be 8.

AstroNerd · Nov 3, 2015

How did u do the equating to get 8

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InteGrand · Nov 3, 2015

AstroNerd said:
Hey guys, I'm not quite sure how u would solve this so if anyone could help that would be great!

a fathers age is the square of his sons 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?

Thanks

Sent from my Nexus 5 using Tapatalk

$Let the father's age today be $f$ years and the son's age today be $s$ years.$

$We are given that:$

$$f=s^2 $ \ \ (1)$

$$f + 20 = 3(s+20)$ \ \ (2)$

$Substitute the expression for $f$ from (1) into (2):$

$\begin{align*} s^2 + 20 &= 3(s+20) \\ \Rightarrow s^2 + 20 &= 3s + 60\\ \Rightarrow s^2 -3s -40 &= 0 \\ \Rightarrow (s-8)(s+5) &= 0.\end{align*}$

$Taking the positive solution, we have $s = 8$. So $f = 8^2 = 64$. So the son is 8 years old and the father is 64 years old (big gap!).$

AstroNerd · Nov 3, 2015

Thanks heaps!

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Quadratic word problem (1 Viewer)

AstroNerd

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nerdasdasd

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InteGrand

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