Question

Solving Linear Equations Unit Test 14 of 1914 of 19 Items Question At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point) The songs will have the same number of listens after days.

Answer 1

To solve the problem, we need to set up equations for the number of listens for both songs over time.

Let \( x \) be the number of days after the beginning of the month.

For the first song:
- Initial listens = 700
- New listens per day = 52

The equation for the first song can be written as:
\[
\text{Listens}_1 = 700 + 52x
\]

For the second song:
- Initial listens = 600
- New listens per day = 56

The equation for the second song can be written as:
\[
\text{Listens}_2 = 600 + 56x
\]

We want to find the value of \( x \) when both songs have the same number of listens:
\[
700 + 52x = 600 + 56x
\]

Now, we can 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 the two songs will have the same number of listens after **25 days**.

Thus, the answer is:
The songs will have the same number of listens after **25 days**.