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

Question

as your variable.

Answer 1

To find the number of days it would take for the two songs to have the same number of listens, we can set up an equation based on the information provided.

Let's define:

• The first song starts with 1,000 listens and gains 38 listens per day.
• The second song starts with 900 listens and gains 40 listens per day.

We can express the number of listens for each song as a function of \( x \), where \( x \) is the number of days.

For the first song: \[ \text{Listens for Song 1} = 1000 + 38x \]

For the second song: \[ \text{Listens for Song 2} = 900 + 40x \]

To find out when the two songs have the same number of listens, we can set these two expressions equal to each other:

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

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

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

2. Subtract 900 from both sides: \[ 100 = 2x \]

3. Divide both sides by 2: \[ x = 50 \]

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

Answer 2

turn that into an equation

Answer 3

Certainly! The equation representing the scenario in which the number of listens for both songs will be equal can be written as:

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

Where:

• \(1000\) is the initial listens of the first song,
• \(38x\) is the additional listens gained by the first song after \(x\) days,
• \(900\) is the initial listens of the second song,
• \(40x\) is the additional listens gained by the second song after \(x\) days.

This equation can be solved to find the value of \(x\) that shows how many days it will take for both songs to have the same number of listens.