Let $x$ represent the number of weeks needed to save $500.

The teenager saves $25 per week, so after $x$ weeks, they will have saved $25x$ dollars.

We set up the equation: $25x = 500$

Now, solve for $x$:

1. Divide both sides by 25: $x = \frac{500}{25}$

2. Calculate: $x = 20$

So, it will take 20 weeks for the teenager to save $500.

Would you like a further breakdown of this solution, or do you have any other questions?

Here are some related questions that might interest you:

1. What if the teenager increases their savings to $30 per week?
2. How much would they have saved after 10 weeks?
3. If they wanted to reach their goal in 15 weeks, how much would they need to save each week?
4. How many weeks would it take to save $750 at the same weekly savings rate?
5. If they receive an extra $50 from a gift, how would that affect the time needed?

Tip: When solving word problems, clearly define your variables and set up an equation based on the information given.