An algebra problem by Cosmic Curiosity

Algebra Level 2

A lad was asked his age by his friend . The lad said, "The number you get when you subtract 25 times my age from twice the square of my age will be thrice your age". If the friend's age is 14, then the age of the lad is :

21 14 25 28 17

Cosmic Curiosity by Cosmic Curiosity , 16, India

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1 solution

Let m m be the present age of the lad.

2 m 2 − 25 m = 3 ( 14 ) = 0 2m^2-25m=3(14)=0

2 m 2 − 25 m − 42 = 0 2m^2-25m-42=0

Now solve for m m using the quadratic equation.

m = 25 ± ( − 25 ) 2 − 4 ( 2 ) ( − 42 ) 2 ( 2 ) = 25 4 ± 31 4 m=\dfrac{25\pm\sqrt{(-25)^2-4(2)(-42)}}{2(2)}=\dfrac{25}{4}\pm \dfrac{31}{4}

Using the positive value, we get

m = 25 4 + 31 4 = 56 4 = m=\dfrac{25}{4}+\dfrac{31}{4}=\dfrac{56}{4}= 14 \boxed{14}

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