In 4 years, Phil will be half Tim's age. Two years ago, Tim was 5 times Phil's age. How old is Phil?

Question

Age problem need to solve for present when only past and future data are provided.

Answer 1

Let p = Phil's current age

Let t = Tim's current age

 

In 4 years Phil will be p+4 years old and Tim will be t+4 years old

2 years ago Phil was p-2 years old and Tim was t-2 years old

 

In 4 years, Phil will be half Tim's age:

p+4 = (1/2)(t+4)

2p + 8 = t + 4

2p - t = -4        {equation  1}

 

Two years ago, Tim was 5 times Phil's age:

t - 2 = 5(p-2)

t - 2 = 5p - 10

-5p + t = -8    {equation 2}

 

Add the two equations to eliminate t and solve for p

 

2p - t = -4

-5p+t = -8

-----------------

-3p = -12

p = 4

 

Phil is 4 years old

 

Substitute the value 4 for p in either equation 1 or equation 2 to find Tim's current age