Fox and Hen
A hen and a fox have a combined age of 91.
The fox is now twice the age of the hen when the fox was as old as the hen is now.
How old are they?
(This puzzle found on the back of a beermat).
posted by steven | 11:26 PM
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3 Comments:
hen:39
fox:52
thx for the puzzle, plep.
Yep.
f + h = 91.
therefore f = 91 - h
f = 2(h - (f - h) )
91 - h = 2(h - (91 - h - h) )
etc.
- plep
Assume:
age of hen now = a
age difference = b
age of fox now = a + b
age of hen then = c
Age of hen now add age of fox now is 91:
(a) + (a + b) = 91
a + a + b = 91
2a + b = 91 -- (1)
Fox is now twice as hold as the hen was:
a + b = 2c -- (2)
"Fox was as old as the hen is now:" Hen is a, so fox was a too; hen was c; age difference is b:
a = c + b
c = a - b -- (3)
substitute (3) into (2):
a + b = 2(a - b)
a + b = 2a - 2b
b = a - 2b
3b = a
a = 3b -- (4)
substitute (4) into (1):
2(3b) + b = 91
6b + b = 91
b = 91/7
b = 13
======
substitute b into (1):
2a + 13 = 91
a = (91 - 13)/2
a = 39
======
Age of hen is a = 39
Age of fox is a + b = 39 + 13 = 52
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