A linear model can describe a total made of a per-item cost and a fixed amount. A phrase like “more than a multiple of ” tells you to multiply first, then add to get . Keep the fixed amount separate from the per-item cost: swapping them changes what the equation says.
Hints
- Hint 1
In a linear model, the amount that repeats gets multiplied by the input. Here, each class contributes the same amount to the cost. Which number should multiply ?
- Hint 2
A fixed amount does not depend on how many classes you take. The phrase “more than” tells you whether to add or subtract that amount from the class-based cost.
Step-by-step
Translate the cost into an equation
Step 1Find the cost that depends on classes
No Desmos needed. The words give the model’s two parts directly. The rate is the cost for each class. “3 times” the number of classes makes the class-based cost .
- Step 2
Add the fixed amount
The total is 12 dollars more than the class-based cost, so add once. Since means the total monthly cost, write:
The per-class amount multiplies ; the fixed amount is added once. This equation models the gym’s monthly cost. Choice D.