At the beginning of the month a song on a streaming service had 700 listens and it was gettign 52 listens each day meanwhile a different song had 600 listens and it was getting 56 new listens each day when will the two song shave the same number of listens

Answer 1

Let's denote the number of days since the beginning of the month as \( x \).

The first song starts with 700 listens and gains 52 listens per day, so the total listens for the first song after \( x \) days will be: \[ 700 + 52x \]

The second song starts with 600 listens and gains 56 listens per day, so the total listens for the second song after \( x \) days will be: \[ 600 + 56x \]

We need to find out when the two songs will have the same number of listens: \[ 700 + 52x = 600 + 56x \]

Now, we'll solve for \( x \):

1. Subtract \( 52x \) from both sides: \[ 700 = 600 + 4x \]

2. Subtract 600 from both sides: \[ 100 = 4x \]

3. Divide by 4: \[ x = 25 \]

So, after 25 days, both songs will have the same number of listens. To find the day of the month when this occurs, you simply need to add 25 days to the beginning of the month. Therefore, if the month has at least 25 days, they'll have the same number of listens on the 25th day of the month.