A fixed fee plus a charge for each item gives a linear inequality when spending has a limit. Add the fee once, multiply the per-item charge by the item count, and use for “no more than.” In Desmos, find the boundary where cost equals the budget. For a greatest whole-number count, move down from a noninteger boundary rather than rounding up.
Hints
- Hint 1
The monthly cost has two parts: the subscription is paid once, while the rental charge repeats for every movie. If counts movies, how would you write the total cost?
- Hint 2
The phrase no more than means the total can equal the budget but cannot exceed it. The boundary is where the cost equals the budget. What equation finds that movie count?
- Hint 3
Movies come in whole numbers. If the boundary falls between two whole numbers, which one is the greatest count that stays within the budget?
Step-by-step
Find the spending cutoff
Step 1Write the monthly cost limit
Let count movies. The $8 subscription is paid once, and each movie adds $2.50, so the cost is . “No more than” means that cost can equal $25 but cannot exceed it. Write the inequality, a comparison that allows a range of values: .
- Step 2
Find where the cost reaches the budget
Find the boundary by making the cost equal $25. Type in Desmos. Here stands for the movie count, and asks Desmos to find where the two sides match. Under PARAMETERS, it shows . That’s the spending cutoff.
- Step 3
Choose the greatest allowed whole number
Each movie makes the cost go up, so the limit allows . You can’t rent part of a movie. The greatest whole number at or below is ; rounding up to would go over the budget. Jenna can rent at most movies. Choice B.