after 5 years, the age of a father will be triple the age of his son, while 5 years ago, he was 7 times as old as his son was. Find their present ages. linear equation in one variable.
Answers
Answer :
The present age of father = 40 years
the present age of his son = 10 years
Step-by-step explanation :
Given :
- After 5 years, the age of a father will be triple the age of his son
- 5 years ago, he was 7 times as old as his son was.
To find :
the present ages if father and son
Solution :
Let the present age of father be x years
and the present age of his son be y years
After 5 years,
father's age = (x + 5) years
his son's age = (y + 5) years
age of father = 3 times son's age
x + 5 = 3(y + 5)
x + 5 = 3y + 15
x - 3y = 15 - 5
x - 3y = 10
x = 10 + 3y ⇒ eqn.[1]
5 years ago,
father's age = (x - 5) years
his son's age = (y - 5) years
age of father = 7 times son's age
x - 5 = 7(y - 5)
x - 5 = 7y - 35
7y - x = 35 - 5
7y - x = 30
Substitute x = 10 + 3y [eqn. 1 ]
7y - (10 + 3y) = 30
7y - 10 - 3y = 30
4y = 30 + 10
4y = 40
y = 40/4
y = 10
x = 10 + 3y
x = 10 + 3(10)
x = 10 + 30
x = 40
Therefore,
the present age of father = 40 years
the present age of his son = 10 years