I am just a layman

Algebra Level 2

While standing at the train station I met two men. They seemed to be quite intelligent. As the train was late, I thought of approaching them. I asked them their ages and one replied, "The difference of our ages is 30". The other one replied, "The product of our ages is 1624". I could not understand their reply as I was just a layman. Can you find the sum of their ages?


The answer is 86.

Ratul Pan by Ratul Pan , 21, India

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2 solutions

Md Zuhair
Feb 25, 2017

Truely speaking, I also couldnt Solve their ages at the train station then

First of all Say their ages are x and y such that x>y

Now,

x-y=30

And xy=1624

Now Squaring the first equation and adding 4 x y 4xy to its each side we get

x 2 + y 2 + 2 x y x^2+y^2+2xy = 900 + 4 *1624 So ( x + y ) 2 = 8 6 2 (x+y)^2 = 86^2

Or x + y = 86 \boxed{x+y = 86}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Zach Abueg
Feb 25, 2017

x − y = 30 ⟹ x = y + 30 x - y = 30 \Longrightarrow x = y + 30

x y = 1624 ⟹ y ( y + 30 ) = 1624 ⟹ y 2 + 30 y − 1624 = 0 ⟹ y = − 58 , 28 xy = 1624 \Longrightarrow y(y + 30) = 1624 \Longrightarrow y^2 + 30y - 1624 = 0 \Longrightarrow y = -58, 28

y = − 58 y = -58 is an extraneous solution, so y = 28 y = 28 .

x = y + 30 = 28 + 30 = 58 x = y + 30 = 28 + 30 = 58

x + y = 58 + 28 = 86 x + y = 58 + 28 = \boxed{86}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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