(a) If José makes 400 minutes of long distance calls for the month, which plan costs less?
(b) For what number of long distance minutes do the two plans cost the same?
If the time spent on long díganme calls is less than this amount, which plan costs less?
To determine which plan costs less for José, we first need to calculate the total cost for each plan based on the number of long distance minutes José uses.
Plan A:
- Base charge: $20
- Cost per minute: $0.10
Total cost for Plan A = $20 + $0.10 * 400 minutes = $20 + $40 = $60
Plan B:
- Charge for first 200 minutes: $15
- Charge for additional minutes: $0.08
Total cost for Plan B = $15 + $0.08 * (400 - 200) = $15 + $0.08 * 200 = $15 + $16 = $31
(a) Plan B costs less for José if he makes 400 minutes of long distance calls for the month.
(b) To determine the number of minutes for which the two plans cost the same, we set the total cost of both plans equal to each other and solve for the number of minutes:
$20 + $0.10x = $15 + $0.08(x-200)
$20 + $0.10x = $15 + $0.08x - $16
$0.02x = $1
x = 50
Therefore, the two plans cost the same for 50 additional minutes beyond the 200-minute limit in Plan B. For any number of minutes less than 250, Plan B would cost less.