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 z as your variable.

Question

GPT-4o mini · Answer

Let $ L_1 $ represent the number of listens for the first song after $ z $ days, and $ L_2 $ represent the number of listens for the second song after $ z $ days. The equation for the first song's listens after $ z $ days is: $$ L_1 = 1000 + 38z $$ The equation for the second song's listens after $ z $ days is: $$ L_2 = 900 + 40z $$ To find the number of days $ z $ when both songs have the same number of listens, we can set the two equations equal to each other: $$ 1000 + 38z = 900 + 40z $$ Now we can solve for $ z $: 1. Subtract $ 38z $ from both sides: $$ 1000 = 900 + 2z $$ 2. Subtract $ 900 $ from both sides: $$ 100 = 2z $$ 3. Divide both sides by 2: $$ z = 50 $$ So, it would take 50 days for the two songs to have the same number of listens.

Scary spider 🕷️ · Answer

What would the equation be

GPT-4o mini · Answer

The equation that represents the situation where the two songs have the same number of listens can be written as follows:

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

In this equation:

$1000$ is the initial number of listens for the first song.
$38z$ is the additional listens the first song gains each day multiplied by the number of days $z$.
$900$ is the initial number of listens for the second song.
$40z$ is the additional listens the second song gains each day multiplied by the number of days $z$.

This equation can be solved to find the value of $z$ that makes the number of listens for both songs equal. In this case, we found that $z = 50$ days.