To determine the correct equation that represents the cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Workout Gym, let's analyze the given pricing structure:
1. Initial Fee: There is a fixed initial fee of \[tex]$15.
2. Daily Cost: There is an additional cost of \$[/tex]1 for each day you use the gym.
To find the total cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days, we need to account for both the initial fee and the daily cost. Here's the step-by-step breakdown:
### Step-by-Step Solution
1. Identify the initial fixed fee:
- Regardless of the number of days you use the gym, you start with an initial fee of \[tex]$15.
2. Identify the variable cost:
- The cost per day is \$[/tex]1.
3. Set up the equation:
- Let [tex]\( c \)[/tex] represent the total cost.
- Let [tex]\( d \)[/tex] represent the number of days.
4. Combine the fixed and variable costs:
- The total cost [tex]\( c \)[/tex] is composed of the initial fee plus the daily costs:
[tex]\[
c = (\text{initial fee}) + (\text{daily cost} \times \text{number of days})
\][/tex]
5. Substitute the values:
- Initial fee is \[tex]$15.
- Daily cost is \$[/tex]1.
- Therefore:
[tex]\[
c = 1d + 15
\][/tex]
### Conclusion
The equation that represents the total cost [tex]\( c \)[/tex] for [tex]\( d \)[/tex] days at Workout Gym is:
[tex]\[
c = 1d + 15
\][/tex]
Or written more simply as:
[tex]\[
c = d + 15
\][/tex]
Among the given options, the correct one is:
[tex]\( c = d + 15 \)[/tex]
