Let's break down the costs involved in joining Healthy Gym to find the correct equation that represents the total cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days.
1. Initial Fee: There is a one-time initial fee of \[tex]$5.
2. Daily Cost: In addition to the initial fee, there is a daily cost of \$[/tex]2 for each day [tex]\( d \)[/tex].
To calculate the total cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Healthy Gym, we need to combine these two costs:
1. Initial Fee: This is a fixed cost of \$5.
2. Daily Cost: This cost depends on the number of days you use the gym. For [tex]\( d \)[/tex] days, the daily cost can be expressed as [tex]\( 2d \)[/tex] dollars.
Thus, the total cost [tex]\( c \)[/tex] can be represented as the sum of the initial fee and the daily cost:
[tex]\[
c = \text{initial fee} + \text{(daily cost per day) \(\times\ d\)}
\][/tex]
Substituting the given values:
[tex]\[
c = 5 + 2d
\][/tex]
Rewriting this equation, we get:
[tex]\[
c = 2d + 5
\][/tex]
Therefore, the equation that represents the total cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Healthy Gym is:
[tex]\[
c = 2d + 5
\][/tex]
So, the correct option is:
[tex]\[
c = 2d + 5
\][/tex]
