Petra is 4 times as old as Philippa. In 8 years time she will be 5 times as old as Philippa. How old are Philippa and Petra?
2 Answers
The question as given has no positive solutions.
If the
Explanation:
The question as given has no positive solutions.
Let Petra's current age be
We are given:
#x = 4y#
#x+8 = 5(y + 8) = 5y + 40#
Subtract the first of these equations from the second to get:
#8 = x+8 - x = 5y+40 - 4y = y + 40#
Subtract
#y = -32#
Then
#x = 4y = 4(-32) = -128#
So Petra is
Alternative problem
Suppose the
Then we are given:
#x = 5y#
#x + 8 = 4(y+8) = 4y + 32#
Subtract the second equation from the first to get:
#-8 = x - (x + 8) = 5y - (4y + 32) = y - 32#
Add
#y = -8 + 32 = 24#
Then
#x = 5y = 5*24 = 120#
So Petra is
Petra = -32, Philippa = 94
Given that initial condition year is
Explanation:
I gave the wrong answer originally. Submission deleted!
Hopefully I will not get interrupted this time!!! Wrong, 4th attempt!
Let current time be
Let time in 8 years be
Let Petra be
Let Philippa be
At
Then
At
Then
Subtract ( 1 ) from ( 2 ) giving:
So
( at first this looks as though it is not possible. However if you view negative age as to be born in the future then it works. So -32 means that
If at
(-32), 32, 32, 32
So