Plz do all the questions
Answers
Question 1 :-
Given :-
- Aaron is 5 years younger than Ron
- Four years later, Ron will be twice as old as Aaron.
To find :-
Their present ages
From the above Statements, we can conclude that Aaron is younger than Ron.
Let Aaron's present age be x.
According to the question,
Ron = x + 5 years old
After 4 years,
Aaron = x + 4 years old
Ron = 2(x+4) = 2x + 8 years old.
If Ron's age 4 years ago was x + 5, then after 4 years, his age will be x + 5 + 4 = x + 9.
Hence by forming the Linear Equation,
x + 9 = 2x + 8
Transposing all the variables to one side and constants to the other,
9 - 8 = 2x - x
1 = x
Substituting x for 1,
Aaron's age = 1
Ron's age = 6
Verification :-
In the linear equation, substituting x for 1,
x + 9 = 2x + 8
1 + 9 + 2(1) + 8
10 = 2 + 8
LHS = RHS
Hence verified
Question 2 :-
Given :-
- Robert's father is 4 times as old as Robert
- After 5 years, father will be 3 times as old as Robert
To find :-
Their present ages
Let Robert's age be y
According to the question,
Robert = y
Robert's father = 4(y) = 4y
After 5 years,
Robert = y + 5
Robert's father = 3(y+5) = 3y + 15
If Robert's father's age is 4y before 5 years, after 5 years his age will be 4y + 5
By forming the Linear Equation,
4y + 5 = 3y + 15
Transposing all the variables to one side and constants to the other,
4y - 3y = 15 - 5
y = 10
Substituting y for 10,
Robert = 10 years old
Robert's father = 4(10) = 40 years old
Verification :-
Substituting y for 10 in the linear equation,
4y + 5 = 3y + 15
4(1) + 5 = 3(10) + 15
40 + 5 = 30 + 15
LHS = RHS
Hence verified