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 your variable.

Question

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 your variable.

Answer 1

Let's assume that after x number of days, both songs will have the same number of listens.

Thus, the equation representing the number of listens for the first song after x days is: 1000 + 38x.
Similarly, the equation representing the number of listens for the second song after x days is: 900 + 40x.

Setting these two equations equal to each other, we have:
1000 + 38x = 900 + 40x.

Simplifying the equation, we get:
38x - 40x = 900 - 1000,
-2x = -100.

Dividing both sides by -2, we find:
x = 50.

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

Answer 2

To write an equation to show the number of days it would take for the two songs to have the same number of listens, we need to consider the initial number of listens for each song and the number of new listens each day for each song.

Let's use "x" as the number of days.

For the first song:
Initial number of listens = 1,000
Number of new listens each day = 38

The total number of listens for the first song after "x" days can be calculated by adding the initial number of listens to the product of the number of new listens per day and the number of days:

Total number of listens for the first song = 1,000 + 38x

For the second song:
Initial number of listens = 900
Number of new listens each day = 40

Similarly, the total number of listens for the second song after "x" days can be calculated using the same formula:

Total number of listens for the second song = 900 + 40x

To find when the two songs have the same number of listens, we can set the two equations equal to each other and solve for "x":

1,000 + 38x = 900 + 40x

Now we can subtract 900 from both sides of the equation:

100 + 38x = 40x

Next, subtract 38x from both sides of the equation:

100 = 2x

Finally, divide both sides of the equation by 2:

x = 50

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

Answer 3

To find the number of days it would take for the two songs to have the same number of listens, you can set up an equation using the given information.

Let's define the number of days as "x".

For the first song, with 1,000 listens at the beginning of the month and 38 new listens each day, the equation would be:
Listens for first song = 1,000 + 38x

For the second song, with 900 listens at the beginning of the month and 40 new listens each day, the equation would be:
Listens for second song = 900 + 40x

Setting these two equations equal to each other, we have:
1,000 + 38x = 900 + 40x

Now you can solve this equation to find the value of "x", which represents the number of days it would take for the two songs to have the same number of listens.