Answer:
at least 500 minutes
Explanation:
The first plan costs 10¢ per minute more, but the second plan has a fixed charge of $49.95. So, the first plan will cost $49.90 more in per-minute charges after 499 minutes are used. It would still be cheaper for that usage.
However, if you were to use 500 minutes, the first plan would cost $50.00 more for minutes used, slightly more than the $49.95 up-front charge of the second plan.
That is, the second plan would be preferable for 500 or more minutes.
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If you let m represent the number of minutes used, then ...
plan 1 charges = 0.18·m
plan 2 charges = 49.95 + 0.08·m
If we want plan 2 charges to be less than plan 1 charges, we must have m satisfy ...
plan 2 charges < plan 1 charges
49.95 + 0.08m < 0.18m . . . . . substitute the rate expressions
49.95 < 0.10m . . . . . . . . . . . . . subtract .08m
499.5 < m . . . . . . . . . . . . . . . . . multiply by 10
Since charges are for whole minutes, this means m ≥ 500.