...35, find their present age
Answers (3)
It's in breaking down the keywords to mathematical expressions.
X = john, Y = harry, Y' = harry past.
Y' = Y - (X - Y)
X = 2 * Y'
X + Y = 35
Then solve.
To explain Y': If for example alice is 30 and bob's 18, when did alice turn 18? Answer's 30 - 18 = 12 years ago; What age was bob 12 years ago? 18 - 12 = 6yo.
I -am- (X =) -twice- (* 2) as old as -you were- (Y') when -I was- (X) -as old as you- (-> Y).
John said to Harry, "I am twice as old as you were when I was as old as you [are now]." (Disambiguation)
J := John's age now
H := Harry's age now
h := Harry's age, when John was as old as Harry is now
If
J = 2h
AND
h = H - (J - H) = 2H - J
THEN
J = 2(2H - J) = 4H - 2J
Now we can set up our system of equations:
3J - 4H = 0
J + H = 35
(3/4)J - H = 0
J + H = 35 ;; add both equations
(7/4)J = 35
7J = 140
J = 20.
35 - 20 = 15.
So, Johnny is 20 and Harry is 15 years old.
There is, of course, a simpler solution without the simultaneous system:
Again, let
J := John's age now
H := Harry's age now
h := Harry's age, when John was as old as Harry is now
Then it took Harry, say, x years from h to H. And it took John the exact same x years from H to J.
h + x = H
H + x = J
So,
h + 2x = J
And, as we know
2h = J
it follows:
h + 2x = 2h
2x = h, and immediately
J = 4x
As h = 2x and h + x = H, it is clear that
H = 3x.
And, as J + H = 35
4x + 3x = 35
7x = 35
x = 5
H = 3x = 15 ;; Harry is 15 yr old
J = 4x = 20 ;; John is 20 yr old.