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.
Write a three paragraph highly detailed and easy to understand explanation of the words above, furthermore, add definitions of words and the answer.
Also, use x as the variable.
The given information states that at the beginning of the month, one song had 1,000 listens and was gaining 38 new listens each day. Let's represent the number of days as "x". Therefore, the total number of listens for this song after "x" days can be represented by the equation 1000 + 38x. Similarly, for the second song, which had 900 listens and was gaining 40 new listens each day, the total number of listens after "x" days can be represented by the equation 900 + 40x.
To determine the number of days it would take for the two songs to have the same number of listens, we need to find when the two equations are equal. So, we set them equal to each other and solve for "x":
1000 + 38x = 900 + 40x
By rearranging the equation, we have:
40x - 38x = 1000 - 900
2x = 100
x = 50
Hence, it would take 50 days for the two songs to have the same number of listens.
In summary, the given information provides the initial number of listens for two songs and the amount of new listens they receive each day. By setting up equations representing the total number of listens after "x" days for each song and equating them, we can solve for the value of "x" to determine the number of days it would take for both songs to have the same number of listens. In this case, it would take 50 days for the two songs to have the same number of listens.
Write a three paragraph highly detailed and easy to understand explanation of the words above, furthermore, add definitions of words and the answer.
Also, use x as the variable.
Sure! Here's a more detailed explanation using the definitions of words and the variable "x":
In this problem, we are given information about two songs on a streaming service. The first song already had 1,000 listens at the beginning of the month and was gaining an additional 38 listens each day. We can represent the total number of listens for this song after "x" days as the equation 1000 + 38x. The second song, on the other hand, had 900 listens initially and was gaining 40 listens per day. The total number of listens for this song after "x" days can be represented as the equation 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 set the two equations equal to each other and solve for "x". By doing this, we can determine when the total number of listens for both songs will be equal. So, our equation becomes 1000 + 38x = 900 + 40x. We then rearrange the equation to isolate the variable and perform the necessary calculations. In this case, after simplifying the equation, we find that x = 50.
Therefore, it would take 50 days for the two songs to have the same number of listens. This means that after 50 days, both songs would have an equal number of total listens, accounting for the initial number of listens and the additional listens gained each day.
give an equation
Sure! The equation that represents the number of listens for the first song after "x" days can be written as:
Number of listens for the first song = 1000 + 38x
Similarly, the equation representing the number of listens for the second song after "x" days can be written as:
Number of listens for the second song = 900 + 40x
These two equations represent the total number of listens for each song after a certain number of days, taking into account the initial number of listens and the additional listens gained each day.
show the equation alone!
The equation representing the number of listens for the first song after "x" days is:
1000 + 38x
And the equation representing the number of listens for the second song after "x" days is:
900 + 40x
the equation without explaanation
Equation for the first song: 1000 + 38x
Equation for the second song: 900 + 40x
To solve this problem, let's break it down step by step. We are given that at the beginning of the month, one song already had 1,000 listens and was getting an additional 38 listens each day. Another song already had 900 listens and was getting 40 new listens each day. We need to find the number of days it would take for the two songs to have the same number of listens.
Let's represent the number of days it takes for the two songs to have the same number of listens as 'x'. Now let's break down the equation for each song. The first song had 1,000 listens initially and then gained 38 new listens each day. So the equation for the number of listens for the first song would be 1,000 + 38x.
The second song had 900 listens initially and then gained 40 new listens each day. Therefore, the equation for the number of listens for the second song would be 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 set these two equations equal to each other and solve for x. So we have the equation:
1,000 + 38x = 900 + 40x
Now, let's simplify and solve for 'x'. Subtract 900 from both sides:
100 + 38x = 40x
Next, subtract 38x from both sides:
100 = 2x
Lastly, divide both sides by 2:
50 = x
Therefore, it would take 50 days for the two songs to have the same number of listens.