A gym charges a one-time membership fee of $17 plus $12 for each class attended. If Sarah paid a total of $149, how many classes did she attend?
For “membership plus per-use fee” problems, quickly translate the words into an equation of the form total = fixed fee + (rate × number of uses). Let a variable represent the unknown count (here, number of classes), subtract the fixed fee from the total, then divide by the per-use rate. Finally, do a fast check by plugging your result back into the original cost expression to ensure it matches the given total.
Hints
Identify fixed vs. per-class costs
Separate the one-time membership fee from the cost per class. Which part of the total is fixed, and which part changes with the number of classes?
Write an equation
Let represent the number of classes Sarah attended. How can you write an equation that adds the membership fee and the class costs to equal ?
Solve step by step
Once you have the equation, first remove the fixed fee from , then figure out how many times fits into the remaining amount.
Desmos Guide
Use Desmos to solve the equation numerically
In Desmos, type the expression (149 - 17) / 12 and look at the output. That value is the number of classes that makes the total cost $149.
Step-by-step Explanation
Define the variable and write the equation
Let be the number of classes Sarah attended.
The total amount she pays is the one-time membership fee plus the cost for each class:
- Membership fee: $17
- Class cost: $12 per class, so for classes
So the total cost equation is:
Isolate the term with the variable
Subtract $17 from both sides to get the part that comes just from the classes:
Solve for the number of classes
Now divide both sides by 12 to solve for :
So Sarah attended 11 classes.