Question

Two rock bands are trying to gain more followers on social media. Strong Friday has 88,300 followers and has been gaining 200 each month. Men and Hippos has 79,900 followers and has been gaining 900 each month.
If these trends continue, how long will it take for the two bands to have the same number of followers?
Simplify any fractions.

Answer 1

Let \( t \) be the number of months from now.

For Strong Friday, the number of followers after \( t \) months will be:
\[
88,300 + 200t
\]

For Men and Hippos, the number of followers after \( t \) months will be:
\[
79,900 + 900t
\]

We want to find when the number of followers for both bands is equal:
\[
88,300 + 200t = 79,900 + 900t
\]

To solve for \( t \), we first move all terms involving \( t \) to one side and constant terms to the other side. Rearranging gives us:
\[
88,300 - 79,900 = 900t - 200t
\]
This simplifies to:
\[
8,400 = 700t
\]

Next, we divide both sides by 700:
\[
t = \frac{8,400}{700}
\]
Simplifying this fraction:
\[
t = 12
\]

Therefore, it will take **12 months** for the two bands to have the same number of followers.

We can verify this by calculating the number of followers for each band after 12 months:

For Strong Friday:
\[
88,300 + 200 \times 12 = 88,300 + 2,400 = 90,700
\]

For Men and Hippos:
\[
79,900 + 900 \times 12 = 79,900 + 10,800 = 90,700
\]

Since both bands will have 90,700 followers after 12 months, our solution is confirmed. Thus, the answer is:
\[
\boxed{12}
\]