To find the monthly fee [tex]\( m \)[/tex] for the online music streaming service, we need to solve the equation given:
[tex]\[
50.88 = 3.00 + 12m
\][/tex]
Here, [tex]\( 50.88 \)[/tex] represents the total yearly membership fee, [tex]\( 3.00 \)[/tex] is the initial registration fee, and the term [tex]\( 12m \)[/tex] represents the total amount paid in monthly fees over the course of a year.
Step-by-Step Solution:
1. Subtract the initial registration fee from the total yearly fee:
To isolate the monthly fees summed for the year, we first subtract the initial registration fee from the total yearly membership fee:
[tex]\[
50.88 - 3.00 = 12m
\][/tex]
2. Calculate the result of the subtraction:
[tex]\[
47.88 = 12m
\][/tex]
3. Solve for [tex]\( m \)[/tex] (the monthly fee) by dividing both sides of the equation by 12:
[tex]\[
m = \frac{47.88}{12}
\][/tex]
4. Calculate the division to find the value of [tex]\( m \)[/tex]:
[tex]\[
m = 3.99
\][/tex]
Therefore, the monthly fee [tex]\( m \)[/tex] that each new member pays is [tex]\( \boxed{3.99} \)[/tex].
