Select ALL the correct answers.

Question

Helga teaches dance classes. She charges for the classes as shown below.

Option 1: $80 per month for five classes
Option 2: $900 per year for 60 classes
Option 3: $174 for 12 classes

Calculate the constant of proportionality for each class. Then select the true statements below.

Option 1 costs $1 more per class than option 2 costs per class.
Option 2 and option 3 cost the same amount per class.
Option 3 costs the least amount per class.
Option 3 costs $1 more per class than option 1 costs per class.
Option 1 and option 3 cost the same amount per class.

Answer 1

To calculate the cost per class for each option, we need to divide the total cost by the number of classes for each option.

Option 1: \[ \text{Cost per class} = \frac{80 \text{ dollars}}{5 \text{ classes}} = 16 \text{ dollars per class} \]

Option 2: \[ \text{Cost per class} = \frac{900 \text{ dollars}}{60 \text{ classes}} = 15 \text{ dollars per class} \]

Option 3: \[ \text{Cost per class} = \frac{174 \text{ dollars}}{12 \text{ classes}} = 14.50 \text{ dollars per class} \]

Now, we can summarize the costs per class:

• Option 1: $16 per class
• Option 2: $15 per class
• Option 3: $14.50 per class

Now, let's evaluate each of the statements.

• Option 1 costs $1 more per class than option 2 costs per class.

  • $16 (Option 1) - $15 (Option 2) = $1 (True)

• Option 2 and option 3 cost the same amount per class.

  • $15 (Option 2) ≠ $14.50 (Option 3) (False)

• Option 3 costs the least amount per class.

  • $14.50 (Option 3) < $15 (Option 2) and $14.50 (Option 3) < $16 (Option 1) (True)

• Option 3 costs $1 more per class than option 1 costs per class.

  • $14.50 (Option 3) < $16 (Option 1) (False)

• Option 1 and option 3 cost the same amount per class.

  • $16 (Option 1) ≠ $14.50 (Option 3) (False)

The true statements are:

• Option 1 costs $1 more per class than option 2 costs per class.
• Option 3 costs the least amount per class.