A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages. What are their ages?
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3 guesses to Princess Bride |
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November 27th, 2011 | Category: 
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X = Princess’ age
Y = Prince’s age
(Think genetics XY / XX)
X = Y + 2 {Y – [ (X + Y)/2 – Y]} – X
2X = Y + 2{ Y – [X/2 – Y/2]}
2X = Y + 2{ 3Y/2 -X /2}
2X = Y +3Y -X
3X =4Y
Any ages in these proportions would work…
Princess: 4 – 8 – 12 – 16 – 20 …
Prince: 3 – 6 – 9 – 12 – 15 …
Let’s take Princess 16 and Prince 12
Half the sum of their ages = 14
When the princess was “Half the sum of their ages” = 14 – 12 = 2 years ago
The princes age “when the princess was Half the sum of their ages” = 12 – 10 = 10 years old
Twice “The prince’s age was when the princess was Half the sum of their ages” = 10 x 2 = 20
The princess will be 20 in 4 years
The prince’s age will then be 12 +4 = 16 by then = the current age of the princess (PERFECT)
Great answer, Rool!
We came up with this one:
Princess: a
Prince: b
0.5*(a+b) a – (0.5*(a+b)) = 0.5*a-0.5*b b – (0.5*a-0.5*b) = 1.5*b-0.5*a 3*b-a
(3*b-a) – a = 3*b-2*a b + (3*b-2*a) = 4*b-2*a a = 4*b-2*a or 3*a = 4*b b+10
0.5*b+5 b – (0.5*b+5) = 0.5*b-5 a – (0.5*b-5) = a-0.5*b+5 b = a-0.5*b+5 or a = 1.5*b-5
Now we have two equations:
3*a = 4*b and a = 1.5*b-5.
Substitute “a” in the first equation for the value of “a” from the second equation:
3*(1.5*b-5) = 4*b
Solving this equation, we get:
b=30
Since a = 1.5*b-5:
a=40
So the princess was 40 and the prince was 30 in this scenario.
You’re today’s winner.
The relation comes out to y=(4/3)x
Where x- prince’s age
And y – princess’s age
So there are many possibilities of the answers.
It could be x = 30 and y=40