Final answer:
The cost function C(x) for using x minutes in this cellular package is given. To find the maximum number of calling minutes you can use while keeping your bill at $50 or lower, an inequality is set up and solved. The maximum number of calling minutes is 110 minutes, so none of the given options are correct.
Step-by-step explanation:
The cost function C(x) for using x minutes in this cellular package is given by:
C(x) = 30, if x ≤ 60
C(x) = 30 + 0.40(x - 60), if x > 60
To find the maximum number of calling minutes you can use while keeping your bill at $50 or lower, we need to set up an inequality:
C(x) ≤ 50
If x ≤ 60, then the inequality becomes 30 ≤ 50, which is true.
If x > 60, then the inequality becomes 30 + 0.40(x - 60) ≤ 50.
Simplifying the inequality, we get:
0.40(x - 60) ≤ 20
Dividing both sides by 0.40, we get:
x - 60 ≤ 50
Adding 60 to both sides, we get:
x ≤ 110
Therefore, the maximum number of calling minutes you can use while keeping your bill at $50 or lower is 110 minutes. Since none of the given options are greater than 110 minutes, the correct answer is d) 90 minutes.
Complete question is:
Basic cellular package costs $30 /month for 60 min. of calling with an additional charge of 0.40/minute beyond that time. The cost function C(x) for using x minutes would be:
If you used 60 minutes or less, i.e. if x ≤ 60, then C(x) = 30
If you used more than 60 min i.e. (x - 60) minutes more than the plan came with, you would pay an additional $0.40 for each of those (x -60 ) minutes.Your total bill would be C(x) =30 + 0.40(x - 60).
If you want to keep your bill at $50 or lower for the month with a given cost function, what is the maximum number of calling minutes you can use?
a) 75 minutes
b) 80 minutes
c) 85 minutes
d) 90 minutes