Explanation:
x = number of minutes
the cost function (in c) of the phone company is
cp(x) = 12x
and the cost function of the discount company is
cd(x) = x/2 + 4600 (R46)
we now need to calculate for what x this becomes the same cost :
12x = x/2 + 4600
24x = x + 9200
23x = 9200
x = 400 minutes
she would have to talk for at least 400 minutes long distance per month to make it an even or then better deal.
with 400 minutes being the break-even point.
so, to make it a better deal (not just equal), she has to talk for at least 401 minutes per month.