At the beginning of the month a song on a streaming service already had 1,000 listens and was getting 38 new listens each day. Meanwhile a different song already had 900 listens and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens, use x as the variable

Answer 1

Let \( L_1 \) represent the number of listens for the first song, and \( L_2 \) represent the number of listens for the second song. We can set up the equations for each song as follows:

• For the first song: \[ L_1 = 1000 + 38x \]
• For the second song: \[ L_2 = 900 + 40x \]

To find the number of days \( x \) it will take for both songs to have the same number of listens, we set the two equations equal to each other:

\[ 1000 + 38x = 900 + 40x \]

Now, you can solve for \( x \):

1. Start by subtracting \( 38x \) from both sides: \[ 1000 = 900 + 2x \]

2. Next, subtract \( 900 \) from both sides: \[ 100 = 2x \]

3. Finally, divide both sides by \( 2 \): \[ x = 50 \]

So, it will take 50 days for the two songs to have the same number of listens.