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. what equation can help show the number of days it would take for the two songs to have the same number of listens
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 given information.
Let's assume "x" represents the number of days it would take for the two songs to have the same number of listens.
For the first song, the total number of listens after "x" days can be calculated as:
Total Listens for the First Song = 1,000 + (38 * x)
For the second song, the total number of listens after "x" days can be calculated as:
Total Listens for the Second Song = 900 + (40 * x)
Since we want to find the number of days when the two songs have the same number of listens, we can set up the equation:
1,000 + (38 * x) = 900 + (40 * x)
Simplifying the equation:
38 * x - 40 * x = 900 - 1,000
-2 * x = -100
Dividing both sides of the equation by -2:
x = (-100) / (-2)
x = 50
Therefore, it would take 50 days for the two songs to have the same number of listens.
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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.
Let's define:
- Let x be the number of days it would take for the two songs to have the same number of listens.
- Y1 be the total listens of the first song after x days.
- Y2 be the total listens of the second song after x days.
From the information given, we know that the first song starts with 1,000 listens and gains 38 new listens each day:
Y1 = 1,000 + 38x
Similarly, the second song starts with 900 listens and gains 40 new listens each day:
Y2 = 900 + 40x
To find the number of days it would take for the two songs to have the same number of listens, we need to find the value of x when Y1 = Y2.
Setting Y1 equal to Y2:
1,000 + 38x = 900 + 40x
Now, we can solve this equation to find the value of x.
Let's assume we need "d" days for the two songs to have the same number of listens.
For the first song, the total number of listens after "d" days would be:
1,000 + 38d
For the second song, the total number of listens after "d" days would be:
900 + 40d
We can set these two expressions equal to each other:
1,000 + 38d = 900 + 40d
Then we can solve for "d":
38d - 40d = 1,000 - 900
-2d = 100
d = -50
This is a negative number, which doesn't make sense in this context.
Therefore, the two songs will never have the same number of listens since the second song is gaining listens at a faster rate than the first song.
Well, well, well, looks like we have a musical showdown here! Let's see if I can help you with this equation challenge. We want to find the number of days it would take for the two songs to have the same number of listens, right?
Let's break it down. The first song starts with 1,000 listens and gains 38 new listens each day. So, the equation for the number of listens on any given day for the first song is:
First song's listens = 1,000 + (38 × number of days)
The second song starts with 900 listens and gains 40 new listens each day. So, the equation for the number of listens on any given day for the second song is:
Second song's listens = 900 + (40 × number of days)
Now, we want to find the point where both songs have the same number of listens. So, we can set these two equations equal to each other:
1,000 + (38 × number of days) = 900 + (40 × number of days)
And there you have it! This equation will help you find the number of days it takes for the two songs to have the same number of listens. Just plug in the numbers and solve for the number of days. Good luck, and may the best song win!