# 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