Ansell now is 3 times as old as Bert. Five years from now he will be twice as old as Bert is then. Find both ages.
Present age:
let Bert's age be x
"Ansell now is 3 times as old as Bert"
so Ansell is now 3x
Five years from now:
Bert : x+5
Ansell : 3x+5
"Five years from now he will be twice as old as Bert is then"
3x+5 = 2(x+5)
3x + 5 = 2x + 10
x = 5
Now go back to our definitions to find their present ages.
15
What is the answer
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the age of Ansell is represented by A and the age of Bert is represented by B.
Based on the given information, we can create the following equations:
1) Ansell now is 3 times as old as Bert: A = 3B
2) Five years from now, Ansell will be twice as old as Bert is then: A + 5 = 2(B + 5)
Now we have a system of equations.
To find the ages of Ansell and Bert, we can use the substitution method or the elimination method.
Let's start with the substitution method:
From equation 1: A = 3B
Substitute this value of A into equation 2:
3B + 5 = 2(B + 5)
Now distribute the 2 on the right side of the equation:
3B + 5 = 2B + 10
Next, subtract 2B from both sides of the equation:
3B - 2B + 5 = 2B - 2B + 10
Simplifying the equation:
B + 5 = 10
Subtract 5 from both sides of the equation:
B + 5 - 5 = 10 - 5
Simplifying:
B = 5
Now that we know Bert's age is 5, we can substitute this value back into equation 1 to find Ansell's age:
A = 3B
A = 3(5)
A = 15
So, Ansell is 15 years old and Bert is 5 years old.