Answer:
Ben is currently 60 years old.
Step-by-step explanation:
Let's denote the current ages of Ben and Ishaan as [tex]x[/tex] and [tex]y[/tex], respectively.
Given that Ben is 4 times as old as Ishaan, we can write the equation:
[tex] x = 4y [/tex]
Also, 6 years ago, Ben was 6 times as old as Ishaan. So, 6 years ago, Ben's age was [tex]x - 6[/tex] and Ishaan's age was [tex]y - 6[/tex].
The equation becomes:
[tex] x - 6 = 6(y - 6) [/tex]
Now, we have a system of two equations:
[tex] x = 4y [/tex]
[tex] x - 6 = 6(y - 6) [/tex]
First, solve the first equation for [tex]x[/tex]:
[tex] x = 4y [/tex]
Now, substitute this expression for [tex]x[/tex] into the second equation:
[tex] 4y - 6 = 6(y - 6) [/tex]
Expand and solve for [tex]y[/tex]:
[tex] 4y - 6 = 6y - 36 [/tex]
[tex] 2y = 30 [/tex]
[tex] y =\dfrac{30}{2}[/tex]
[tex] y = 15 [/tex]
Now that we have [tex]y[/tex], substitute it back into the equation [tex]x = 4y[/tex] to find [tex]x[/tex]:
[tex] x = 4 \times 15 = 60 [/tex]
So, Ben is currently 60 years old, and Ishaan is 15 years old.
