A one-time fee paired with a charge “per month” signals a linear cost model: the monthly charge repeats, but the fee does not. Multiply the monthly rate by the number of months, then add the fee once to match the total. Use a Desmos regression to solve for the fee. The trap is multiplying the one-time fee by the number of months too.
Hints
- Hint 1
A monthly rate is charged each month. Multiply the rate by the number of months to find the membership charges alone. The registration fee hasn't been counted yet.
- Hint 2
Let be the one-time fee in dollars. Add one copy of to the membership charges, then set that sum equal to Julio's total payment.
Step-by-step
Separate the monthly charges from the fee
Step 1Find the membership charges
The $25 per month charge repeats for months. Type in Desmos; it shows . That's the cost of the months of membership, before the one-time fee.
- Step 2
Match the charges to Julio's total
Let be the registration fee in dollars. Julio paid the in monthly charges plus the fee paid once, for a total of , so
The monthly rate repeats; the registration fee does not.
- Step 3
Solve for the registration fee
Below in Desmos, type . The tells Desmos to solve for instead of graphing . Under PARAMETERS, it shows . Since is the registration fee, Julio paid for it. Grid in 50.