Question 1104877
There is no great mystery about this problem.
If Navy knew how many minutes she will use per month,
she would just calculate the cost for both providers,
and decide which is best.
Not knowing eactly, she would say she will use {{{x}}} minutes per month.
For that usage, Horizon would charge her {{{15x}}} cents,
or {{{0.15x}}} , in $.
Spirit would charge her {{{$20}}} plus an extra charge of {{{5x}}} cents,
{{{0.05x}}} in $, for the minutes used.
So, the expressions for the monthly cost, in $, would be
{{{S=20+0.05x}}} for Spirit, and
{{{H=0.15x}}} for Horizon.
With that, Navy can graph both expressions with the cost per month as {{{y}}}
as a function of {{{x}}} , the number of minutes:
{{{drawing(300,300,-40,360,-5,45,grid(1),
blue(line(0,0,360,54)),green(line(0,20,360,38))
)}}} The two lines cross at {{{system(blue(y=0.15x),green(y=20+0.05x))}}} --> {{{system(x=200,y=30)}}} .
If Navy is sure she will always use less than 200 minutes,
she should go with Horizon, whose cost, {{{blue(y=0.15x)}}} ,
is represented by the blue line.
If she is sure she will always use more than 200 minutes,
she should go with Spirit, whose cost, {{{green(y=20+0.05x)}}} ,
is represented by the green line.