A gym charges a one-time sign-up fee of $40 and $15 per month for membership. Victoria can spend at most $115 on her membership.
If represents the number of months of membership Victoria can afford, which inequality represents this situation?
For a membership with a one-time charge and a charge per month, find the total cost before comparing it with the budget. A linear inequality shows which costs stay within a limit; “at most” includes the limit itself. Multiply only the charge that repeats by the number of months. Multiplying the sign-up fee instead would charge it every month.
Hints
- Hint 1
A monthly rate repeats each month. Since counts months, multiply the monthly price by . Which fee is charged only once, no matter how many months Victoria joins?
- Hint 2
An upper limit is a ceiling: at most lets the cost equal the budget but not exceed it. How should you compare Victoria’s total cost with the amount she can spend?
Step-by-step
Build the cost inequality
Step 1Find the cost that repeats
No Desmos needed. You’re writing an inequality from the fees, not solving one. The $15 monthly fee is paid for each of months, so those charges total . Only the monthly fee gets multiplied by .
- Step 2
Add the fee paid once
The $40 sign-up fee is paid once, so add it to the monthly charges. Victoria’s total cost is . Multiplying by would charge the sign-up fee every month.
- Step 3
Compare the total with the budget
At most means the total can equal but cannot exceed it, so write:
This inequality represents the months Victoria can afford. Choice C.