How old is Brandon now if Michael is three times his age and 18 years ago Michael was nine times as old as Brandon?

To solve the problem, let’s define the current ages of Michael and Brandon.

Let B be Brandon’s current age. According to the information provided:

• Michael is three times as old as Brandon: M = 3B.
• 18 years ago, Michael was nine times as old as Brandon: M – 18 = 9(B – 18).

Now, we can substitute the first equation into the second equation:

3B – 18 = 9(B – 18)

This simplifies to:

3B – 18 = 9B – 162

Next, let’s move all terms involving B to one side and constant terms to the other side:

3B – 9B = -162 + 18

This results in:

-6B = -144

Now, dividing both sides by -6 gives:

B = 24

So, Brandon is currently 24 years old.

To find Michael’s age, we substitute B back into the first equation:

M = 3B = 3 * 24 = 72

Thus, Michael is 72 years old.

To summarize:

Brandon’s current age is 24 years old and Michael’s current age is 72 years old.