To find the equation that represents the cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Healthy Gym, we need to understand the structure of their fee.
1. Initial Fee: There is an initial fee of \[tex]$5. This is a one-time fee that does not depend on the number of days.
2. Daily Fee: There is a daily fee of \$[/tex]2. This fee applies for each day you use the gym.
To express the total cost [tex]\( c \)[/tex] for using the gym for [tex]\( d \)[/tex] days, we need to add the initial fee and the total cost from the daily fees.
Step-by-step, we proceed as follows:
1. Calculate the total daily fee: Since the daily fee is \$2 per day, for [tex]\( d \)[/tex] days, the daily fee would be [tex]\( 2 \times d \)[/tex].
2. Add the initial fee: The total cost [tex]\( c \)[/tex] combines the initial fee and the total daily fee. Therefore, the cost is given by:
[tex]\[
c = \text{initial fee} + \text{total daily fee}
\][/tex]
Plugging in the values:
[tex]\[
c = 5 + 2d
\][/tex]
So, the correct equation that represents the cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Healthy Gym is:
[tex]\[
c = 2d + 5
\][/tex]
Thus, the correct answer from the provided options is:
[tex]\[
c = 2d + 5
\][/tex]
