A linear cost model adds a fee paid once to a charge that repeats for each mile. Build the total cost, then compare it with the budget using the inequality signaled by at most. Subtracting the fee treats it like a discount; reversing the inequality turns a spending limit into a minimum.
Hints
- Hint 1
A flat fee is paid only once, even if the ride covers no miles. The per-mile charge repeats for every mile. Which amount should you multiply by before adding the two charges?
- Hint 2
An upper limit is the most Raj can spend, not the least he must spend. A ride costing exactly the budget is allowed. Which inequality sign includes that cost and all lower costs?
Step-by-step
Build the cost, then apply the budget
Step 1Write the total cost
No Desmos needed. You're writing a cost limit, not solving a given equation. The $3 flat fee is charged once, and the $2 charge applies to each of the miles. So the total cost, in dollars, is . Don't subtract the fee: it adds to the bill.
- Step 2
Keep the cost within Raj's budget
At most $25 means the total can be $25 or less. An upper limit includes the limit and every amount below it. So . This inequality models the miles Raj can afford. Choice C.