Final answer:
Alice would need to have the first satellite TV plan for 4 months for it to be the better buy, as at this point, the total cost of the first plan ($235) becomes equal to the cost of the second plan ($240) and will be less for any subsequent month.
Step-by-step explanation:
To determine how many months Alice must have the satellite TV plan for the first plan to be the better buy, we need to compare the total costs of both plans over time. The first plan has an initial cost of $115 for equipment and installation, with an additional $30 per month. The second plan has no initial cost but charges $60 per month. We set up an equation to find when the costs of both plans will be equal:
Initial cost + (Monthly cost × Number of months) = Monthly cost of second plan × Number of months
For the first plan: $115 + $30m = $60m (where m is the number of months)
To find the break-even point, we solve for m:
$115 + $30m = $60m
$115 = $60m - $30m
$115 = $30m
m = $115 / $30
m = 3.8333
Since Alice cannot have a fraction of a month, she would need to have the plan for 4 months in order for the first plan to be the better buy.