A subscription service charges a one-time activation fee of dollars and a flat rate of dollars per month. If a customer’s total payment after 8 months is dollars, which equation represents the relationship between and ?
A linear cost model fits a bill with a fixed fee and the same charge each month. Multiply the monthly rate by the number of months, then add the one-time fee to get the total. If the choices show the relationship in a different form, rearrange your equation. Don't multiply the fee by the number of months; it's paid only once.
Hints
- Hint 1
The monthly rate is in dollars per month. Multiply it by the number of months to get the part of the total from monthly payments. What is that amount?
- Hint 2
A fixed charge is paid only once. Add it to the monthly charges to get the total. How would you write that sum using the symbols in the question?
Step-by-step
Build the total, then rearrange
Step 1Find the monthly charges
No Desmos needed. You're writing an equation, and the only calculation is one multiplication. The monthly charge repeats for months, so multiply dollars per month by months: . That's in monthly charges, not the whole payment.
- Step 2
Write the total payment
The one-time fee is dollars, and the total is dollars. So the total is the fee paid once plus the monthly charges: . Don't multiply by ; the fee doesn't repeat.
- Step 3
Match the equation to a choice
Subtract from both sides to leave the monthly charges: . The total payment minus the activation fee is the paid over months. Choice B.