SOLUTION: Can you please help me with this math problem PLEASE! Navy is trying to decide what would be the best cell phone plan for her. She has narrowed her choices down to two. Spirit

Question 1104877: Can you please help me with this math problem PLEASE!
Navy is trying to decide what would be the best cell phone plan for her. She has narrowed her choices down to two. Spirit and Horizon. Spirit has a fixed fee of $20 and an additional charge of 5 cents per minute. Horizon has no fixed fee and charges 15 cents per minute. Form a systems of equation for this problem.
Found 2 solutions by Theo, KMST:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of minutes.

spirit charges 10 + .05 * x.

horizon charges .15 * x

she wants to compare what spirit charges versus what horizon charges and where the break even point would be.

at least i think that's what she wants to do.

both plans will break even when the cost for each plan is the same.

the cost for spirit is 20 + .05 * x

the cost for horizon is .15 * x.

when the cost is even, then 20 + .05 * x = .15 * x

subtract .05 * x from both sides of this equation to get 20 = .10 * x

divide both sides of this equation by .10 to get 20 /.10 = x

solve for x to get x = 200.

the plans will break even when the number of minutes used per month = 200.

if she uses less than 200 minutes, the horizon plan is cheaper.

if she uses more than 200 minutes, the spirit plan is cheaper.

your system of equations is:

cost for spirit plan = 20 + .05 * x.
cost for horizon plan = .15 * x

we'll look at a couple of sample figures.

100 is less than 200.
cost for spirit is 20 + .05 * 100 = 25.
cost for horizon is .15 * 100 = 15.
horizon is cheaper.

200 is equal to 200.
cost for spirit is 20 + .05 * 200 = 30
cost for horizon is .15 * 200 = 30
they break even.

300 is greater than 200.
cost for spirit is 20 + .05 * 300 = 35
cost for horizon is .15 *300 = 45
spirit is cheaper.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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 minutes per month.
For that usage, Horizon would charge her cents,
or , in $.
Spirit would charge her plus an extra charge of cents,
in $, for the minutes used.
So, the expressions for the monthly cost, in $, would be
for Spirit, and
for Horizon.
With that, Navy can graph both expressions with the cost per month as
as a function of , the number of minutes:
The two lines cross at --> .
If Navy is sure she will always use less than 200 minutes,
she should go with Horizon, whose cost, ,
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, ,
is represented by the green line.
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