Two years ago, the annual membership fee at a fitness club was $m. Today, the annual membership fee at the club can be represented by the given expression.

Question

Which set of statements is true?
A.
The annual membership fee at the fitness club decreased by 5%.
An equivalent expression that represents this situation is m − 0.05m.
B.
The annual membership fee at the fitness club decreased by 105%.
An equivalent expression that represents this situation is m − 1.05m.
C.
The annual membership fee at the fitness club increased by 5%.
An equivalent expression that represents this situation is m + 0.05m.
D.
The annual membership fee at the fitness club increased by 105%.
An equivalent expression that represents this situation is m + 1.05m.

Answer 1

Let's analyze each of the statements regarding changes to the annual membership fee.

1. Statement A: "The annual membership fee at the fitness club decreased by 5%. An equivalent expression that represents this situation is m − 0.05m."

   • A decrease of 5% means you pay 95% of the original fee, which can be expressed as: \[ m - 0.05m = 0.95m \]
   • This statement is true.

2. Statement B: "The annual membership fee at the fitness club decreased by 105%. An equivalent expression that represents this situation is m − 1.05m."

   • A decrease of 105% would imply paying back more than what you originally paid, which is nonsensical in this context. The calculation is: \[ m - 1.05m = -0.05m \]
   • This statement is false.

3. Statement C: "The annual membership fee at the fitness club increased by 5%. An equivalent expression that represents this situation is m + 0.05m."

   • An increase of 5% means you pay 105% of the original fee, expressed as: \[ m + 0.05m = 1.05m \]
   • This statement is true.

4. Statement D: "The annual membership fee at the fitness club increased by 105%. An equivalent expression that represents this situation is m + 1.05m."

   • An increase of 105% would mean paying 205% of the original fee, expressed as: \[ m + 1.05m = 2.05m \]
   • This statement is false.

Therefore, the true statements are A and C.

Answer 2

its only one answer

Answer 3

Thank you for your clarification! Given that only one of the options is correct, let’s carefully analyze each again based on the information provided.

1. Statement A:

   • Decrease of 5%: \[ \text{New fee} = m - 0.05m = 0.95m \]
   • This is a correct interpretation of a 5% decrease.

2. Statement B:

   • Decrease of 105%: \[ \text{New fee} = m - 1.05m = -0.05m \]
   • This statement is nonsensical as it implies a negative fee.

3. Statement C:

   • Increase of 5%: \[ \text{New fee} = m + 0.05m = 1.05m \]
   • This is a correct interpretation of a 5% increase.

4. Statement D:

   • Increase of 105%: \[ \text{New fee} = m + 1.05m = 2.05m \]
   • This statement also does not make sense in standard interpretations of fee changes.

Given the context of the question, where only one option should be found to be true:

• Since Statement A presents a viable scenario regarding a decrease in the fee, and is true, and Statement C represents a true increase.

If only one answer must be given, it would depend on what the question specifically represents today’s change in the fee. However, if we are assuming a straightforward decrease or increase:

The correct answer generally chosen in such questions is Statement A when identifying a decrease is the main context. If the context or operations led towards an increase as the main factor, then Statement C could also be seen as true.

So the best fit for the question may ultimately be Statement A about the decrease unless the context indicates otherwise.