y = 96 (fixed annual fee option)
y = 3x (per book borrowed option)
The graph would show two lines intersecting at point (0,0) on the y-axis, with the first line being a horizontal line at y = 96 and the second line being a diagonal line with a slope of 3, passing through the origin.
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.
Here's a graph that shows a system of equations for this scenario where x is the number of books Aaden borrows and y is the total cost of the subscription.
7 answers
What does point Q (50,96) represent in this context?
Point Q (50,96) represents the scenario where Aaden borrows 50 books using the subscription with the fixed annual fee option. This means that his total cost for the subscription would be $96, as he pays the fixed annual fee regardless of how many books he borrows.
A number of books and their cost where the subscription with the annual fee costs less
(Choice B) A number of books and their cost where the subscription that charges per book costs less
B
A number of books and their cost where the subscription that charges per book costs less
(Choice C) A number of books and their cost where both subscriptions cost the same
C
A number of books and their cost where both subscriptions cost the same
(Choice D) A number of books and their cost that is not possible with either subscription
D
A number of books and their cost that is not possible with either subscription
(Choice B) A number of books and their cost where the subscription that charges per book costs less
B
A number of books and their cost where the subscription that charges per book costs less
(Choice C) A number of books and their cost where both subscriptions cost the same
C
A number of books and their cost where both subscriptions cost the same
(Choice D) A number of books and their cost that is not possible with either subscription
D
A number of books and their cost that is not possible with either subscription
If we compare the two subscription options, we see that the subscription with the fixed annual fee of $96 would cost less when the number of books borrowed is less than 32, as 3x > 96 when x < 32.
On the other hand, the subscription that charges per book would cost less when the number of books borrowed is greater than 32, as 3x < 96 when x > 32.
When the number of books borrowed is exactly 32, both subscriptions would cost the same, as 3(32) = 96.
Therefore:
- Choice B: A number of books and their cost where the subscription with the annual fee costs less, would be any number less than 32.
- Choice C: A number of books and their cost where the subscription that charges per book costs less, would be any number greater than 32.
- Choice D: A number of books and their cost that is not possible with either subscription, would be a fractional number of books, as you can't borrow a fraction of a book.
On the other hand, the subscription that charges per book would cost less when the number of books borrowed is greater than 32, as 3x < 96 when x > 32.
When the number of books borrowed is exactly 32, both subscriptions would cost the same, as 3(32) = 96.
Therefore:
- Choice B: A number of books and their cost where the subscription with the annual fee costs less, would be any number less than 32.
- Choice C: A number of books and their cost where the subscription that charges per book costs less, would be any number greater than 32.
- Choice D: A number of books and their cost that is not possible with either subscription, would be a fractional number of books, as you can't borrow a fraction of a book.
choose 1 answer choice
The correct answer choice is:
B. A number of books and their cost where the subscription with the annual fee costs less.
B. A number of books and their cost where the subscription with the annual fee costs less.
2 answers