Crystal Tunes and Mad Musik are competing music streaming sites. Crystal Tunes currently has 7.2 million subscribers and has been gaining 1.7 million subscribers each month. Mad Musik currently has 26.8 million subscribers but has been losing 1.1 million subscribers each month.

Question

If these trends continue, how long will it take for the two streaming sites to have the same number of subscribers?

Answer 1

Let's denote the number of months from now as \( x \).

1. The number of subscribers for Crystal Tunes after \( x \) months will be: \[ 7.2 + 1.7x \]

2. The number of subscribers for Mad Musik after \( x \) months will be: \[ 26.8 - 1.1x \]

We want to find \( x \) when these two expressions are equal, that is: \[ 7.2 + 1.7x = 26.8 - 1.1x \]

Now, let's solve for \( x \):

1. First, add \( 1.1x \) to both sides: \[ 7.2 + 1.7x + 1.1x = 26.8 \] This simplifies to: \[ 7.2 + 2.8x = 26.8 \]

2. Next, subtract \( 7.2 \) from both sides: \[ 2.8x = 26.8 - 7.2 \] So: \[ 2.8x = 19.6 \]

3. Now, divide both sides by \( 2.8 \): \[ x = \frac{19.6}{2.8} \approx 7 \]

Thus, it will take approximately 7 months for Crystal Tunes and Mad Musik to have the same number of subscribers if the trends continue.