Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
The Correct Answer and Explanation is :
To determine which subscription is the most cost-effective, we need to compare the two options based on the number of books Aaden expects to borrow annually.
Subscription Option 1: Fixed Annual Fee
- This subscription charges a fixed $96 annual fee.
- Regardless of how many books Aaden borrows, he will always pay $96 per year.
Subscription Option 2: Pay-Per-Book
- This subscription charges $3 per book borrowed.
- If Aaden borrows xx books, the total cost would be 3x3x dollars.
Finding the Break-Even Point
To find when the costs of the two options are equal, we set the total costs equal to each other: 96=3×96 = 3x
Solving for xx: x=963=32x = \frac{96}{3} = 32
This means that if Aaden borrows 32 books in a year, both subscriptions will cost the same amount — $96.
Comparing the Costs for Different Numbers of Books
- If Aaden borrows fewer than 32 books:
- The fixed annual fee subscription will still cost $96.
- The pay-per-book option will cost 3x3x dollars, where xx is the number of books borrowed. For example, if Aaden borrows 10 books, the cost would be 3×10=303 \times 10 = 30 dollars.
- In this case, the pay-per-book option is cheaper.
- If Aaden borrows more than 32 books:
- The pay-per-book option will cost more than $96. For instance, if Aaden borrows 50 books, the cost would be 3×50=1503 \times 50 = 150 dollars.
- In this case, the fixed annual fee option becomes cheaper.
Conclusion
- If Aaden borrows 32 or more books per year, the fixed annual fee subscription is the better option because it costs $96.
- If Aaden borrows fewer than 32 books, the pay-per-book subscription is cheaper because it costs less than the $96 fixed fee.
Thus, the choice depends on how many books Aaden expects to borrow in a year.