Let's use algebra to represent their current ages and solve the problem. Let's say Liam's current age is L, and Henri's current age is H.
(Answers will be placed at the bottom!)
Currently, Liam is 4 times as old as Henri:
L = 4H
Six years ago, Liam was 10 times as old as Henri:
L - 6 = 10(H - 6)
Now, we have a system of two equations:
L = 4H
L - 6 = 10(H - 6)
Let's solve this system to find their current ages.
Step 1: Substitute the value of L from equation (1) into equation (2):
4H - 6 = 10(H - 6)
Step 2: Distribute the 10 on the right side:
4H - 6 = 10H - 60
Step 3: Move all the H terms to one side by subtracting 4H from both sides:
4H - 4H - 6 = 10H - 4H - 60
-6 = 6H - 60
Step 4: Move the constant term to the other side by adding 60 to both sides:
-6 + 60 = 6H - 60 + 60
54 = 6H
Step 5: Solve for H by dividing both sides by 6:
H = 54 / 6
H = 9
Now that we have Henri's current age (H = 9), we can find Liam's current age using equation (1):
L = 4H
L = 4 * 9
L = 36
Therefore, Henri is currently 9 years old, and Liam is currently 36 years old.