At the beginning of the a song on instrument server head lesson 1000 views and I was getting 88 new listeners each day meanwhile a different song already had 900 lessons and getting new lessons each day. Write an equation to show the number of days it would take for two songs to have the Of lessons

Answer 1

Let's denote the number of lessons for the first song as \( L_1 \) and the number of lessons for the second song as \( L_2 \).

At the beginning:

• The first song (let's call it Song A) has 1000 lessons.
• The second song (let's call it Song B) has 900 lessons.

The growth rate for Song A is 88 new listeners (lessons) per day. Therefore, after \( t \) days, the number of lessons for Song A can be expressed as: \[ L_1(t) = 1000 + 88t \]

The growth rate for Song B isn't specified, but let's assume it gets \( r \) new listeners (lessons) per day. After \( t \) days, the number of lessons for Song B will be: \[ L_2(t) = 900 + rt \]

To find the number of days until both songs have the same number of lessons, we set the two equations equal to each other: \[ 1000 + 88t = 900 + rt \]

Now, rearranging the equation to isolate \( t \): \[ 1000 - 900 = rt - 88t \] \[ 100 = (r - 88)t \]

Solving for \( t \): \[ t = \frac{100}{r - 88} \]

This equation shows the number of days \( t \) it would take for the two songs to have the same number of lessons, given the growth rate \( r \) of Song B.