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