Five years ago, Tom was one third as old as his father was then. In 5 years, Tom will be half as old as his father will be then. Find their ages now. Show your equation

The father is 35years old and the son Tom is 15years old

Step-by-step explanation:

Let the father's be y

Let Tom's age be T

5 years ago:

The father's age is: y - 5

Tom's age:

T - 5.

But Tom's age was one third the father's age. This is written as:

T - 5 = 1/3 (y - 5)

3 (T - 5) = y - 5

3T - 15 = y - 5

3T - y = - 5 + 15

3T - y = 10 (1)

In 5years time:

The father's age is:

y + 5

Tom's age:

T + 5

But in 5years time, Tom will be half as old as his father. This is written as:

T + 5 = 1/2 (y + 5)

2 (T + 5) = y + 5

2T + 10 = y + 5

2T - y = 5 - 10

2T - y = - 5 (2)

Therefore, the equations are

3T - y = 10 (1)

2T - y = - 5. (2)

Solving by elimination method:

Subtract equation (2) from (1)

3T - y = 10

- (2T - y = - 5)

T = 15

Substituting the value of T into equation (1)

3T - y = 10

3 (15) - y = 10

45 - y = 10

45 - 10 = y

y = 35

Therefore,

The father is 35years old and the son Tom is 15years old