Question

michael is 3 times as old as brandon. 18 years ago, michael was 9 times as old as brandon. how old is brandon now?

Explanation:

Step1: Define variables for current ages

Let Brandon's current age be $x$. Then Michael's current age is $3x$.

Step2: Set up equation for past ages

18 years ago, Brandon's age was $x-18$, Michael's age was $3x-18$. Michael was 9 times Brandon's age then:
$$3x - 18 = 9(x - 18)$$

Step3: Expand the right-hand side

$$3x - 18 = 9x - 162$$

Step4: Rearrange to solve for $x$

Subtract $3x$ from both sides:
$$-18 = 6x - 162$$
Add 162 to both sides:
$$144 = 6x$$
Divide by 6:
$$x = \frac{144}{6} = 24$$

Answer:

24