Question
Healthy Gym charges members a fee for each visit, while Fitness Gym charges members a one-time yearly charge plus a fee for each visit. The equations below represent the amounts members pay at each gym, where t represents the total yearly cost and n represents the number of visits.
Healthy Gym: 6n=t
Fitness Gym: 80+4n=t
Which statement about the total yearly cost of the memberships is true?
NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(1 point)
Responses
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost is the same at both gyms when members make 25 visits to each one.
The total yearly cost is the same at both gyms when members make 25 visits to each one.
The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.
The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.
The total yearly cost is $240 at each gym for 40 visits.
The total yearly cost is $240 at each gym for 40 visits.
Healthy Gym: 6n=t
Fitness Gym: 80+4n=t
Which statement about the total yearly cost of the memberships is true?
NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(1 point)
Responses
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost is the same at both gyms when members make 25 visits to each one.
The total yearly cost is the same at both gyms when members make 25 visits to each one.
The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.
The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.
The total yearly cost is $240 at each gym for 40 visits.
The total yearly cost is $240 at each gym for 40 visits.
Answers
GPT-4o mini
To determine which statement is true, we can compare the total yearly costs at both gyms for different numbers of visits.
1. **Healthy Gym** charges:
\[
t = 6n
\]
2. **Fitness Gym** charges:
\[
t = 80 + 4n
\]
We'll analyze the total costs for different scenarios:
1. **When members make 0 visits**:
- Healthy Gym: \( t = 6(0) = 0 \)
- Fitness Gym: \( t = 80 + 4(0) = 80 \)
Here, Fitness Gym is higher.
2. **When members make 25 visits**:
- Healthy Gym: \( t = 6(25) = 150 \)
- Fitness Gym: \( t = 80 + 4(25) = 80 + 100 = 180 \)
Here, Healthy Gym is lower.
3. **When members make 40 visits**:
- Healthy Gym: \( t = 6(40) = 240 \)
- Fitness Gym: \( t = 80 + 4(40) = 80 + 160 = 240 \)
Both costs are equal.
Now, let's analyze the statements:
1. **The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.**
- This is not true because if you do 0 visits, Healthy Gym is lower and for 25 visits, Healthy Gym is lower.
2. **The total yearly cost is the same at both gyms when members make 25 visits to each one.**
- This is not true because they are not the same; Healthy Gym is lower.
3. **The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.**
- This is not true since it varies depending on the number of visits.
4. **The total yearly cost is $240 at each gym for 40 visits.**
- This statement is true, as calculations show both gyms have the same cost of $240 when 40 visits are made.
Therefore, the correct statement is:
**The total yearly cost is $240 at each gym for 40 visits.**
1. **Healthy Gym** charges:
\[
t = 6n
\]
2. **Fitness Gym** charges:
\[
t = 80 + 4n
\]
We'll analyze the total costs for different scenarios:
1. **When members make 0 visits**:
- Healthy Gym: \( t = 6(0) = 0 \)
- Fitness Gym: \( t = 80 + 4(0) = 80 \)
Here, Fitness Gym is higher.
2. **When members make 25 visits**:
- Healthy Gym: \( t = 6(25) = 150 \)
- Fitness Gym: \( t = 80 + 4(25) = 80 + 100 = 180 \)
Here, Healthy Gym is lower.
3. **When members make 40 visits**:
- Healthy Gym: \( t = 6(40) = 240 \)
- Fitness Gym: \( t = 80 + 4(40) = 80 + 160 = 240 \)
Both costs are equal.
Now, let's analyze the statements:
1. **The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.**
- This is not true because if you do 0 visits, Healthy Gym is lower and for 25 visits, Healthy Gym is lower.
2. **The total yearly cost is the same at both gyms when members make 25 visits to each one.**
- This is not true because they are not the same; Healthy Gym is lower.
3. **The total yearly cost at Healthy Gym is about $80 lower than the total yearly cost at Fitness Gym.**
- This is not true since it varies depending on the number of visits.
4. **The total yearly cost is $240 at each gym for 40 visits.**
- This statement is true, as calculations show both gyms have the same cost of $240 when 40 visits are made.
Therefore, the correct statement is:
**The total yearly cost is $240 at each gym for 40 visits.**