Question 140·Medium·Linear Equations in One Variable
A fitness center charges a one-time enrollment fee of dollars plus $12 for each visit. In April, Jamie visited the fitness center 9 times and her total charge for that month was $168.
What was the enrollment fee, in dollars?
For cost word problems with a fixed fee plus a per-unit charge, write an equation in the form total cost = fixed fee + (rate × number of units). Plug in the given numbers, simplify the product, and then isolate the unknown fee using inverse operations (usually subtraction, then division if needed). Finally, quickly check your answer by substituting it back into the original cost description to see if it reproduces the total.
Hints
Separate fixed cost and per-visit cost
First, think about how much Jamie paid just for her 9 visits (not counting the enrollment fee). How do you find that using 12 dollars per visit?
Write an equation for the total cost
Let f be the one-time enrollment fee. Write an equation where f plus the total visit cost equals 168 dollars.
Isolate the unknown fee
Once you have an equation like f + (visit cost) = 168, what operation should you use to get f by itself?
Desmos Guide
Use Desmos to compute the enrollment fee
In an expression line, type 168 - 12*9 and look at the numerical result that Desmos displays; that value is the enrollment fee.
Step-by-step Explanation
Translate the situation into an equation
Jamie pays a one-time enrollment fee f plus 12 dollars for each visit.
In April she visited 9 times, so the visit charges are 12 × 9 dollars.
Total cost = enrollment fee + visit charges, so write the equation:
Simplify the visit charges
Calculate the cost of the 9 visits:
12 × 9 = 108, so the equation becomes
Solve the equation for f
Isolate f by subtracting 108 from both sides:
Compute the difference: 168 − 108 = 60.
So the enrollment fee f is 60 dollars.