Question 1040269: The telephone company offers two types of service with plan A you can make an unlimited number of a local calls per month for $18.50 with Plan B you pay $6.50 monthly Plus $0.10 for each minute of calls after the first 40 minutes at least how many minutes would you have to use the telephone each month to make Plan A the better option? Please help I don't know how to set this up I'm not good at solving word problems.
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! for plan A, the cost per month is 18.50
for plan B, the cost per month is 6.50 + .10 * the number of minutes for all minutes greater than 40.
this can be translated to say:
for plan B, the cost per month is 6.50 if the number of minutes of use is less than 40, ....
and the cost per month is 2.50 + .10 * per minute if the number of minutes of use is greater than 40.
how was the second formula calculated?
if the number of minutes used was exactly 40 minutes, then .10 per minute would have been calculated to be 4.00.
subtract 4.00 from 6.50 and the cost for exactly 40 minutes is 2.50 + .10 * 40 which comes out to be 2.50 + 4.00 = 6.50.
in order for plan A to be the cheaper plan, the number of minutes of use would have to be greater than 40 because it's clear that, if the number of minutes of use was less than or equal to 40, plan A could not possibly be cheaper than plan B.
this tells you that the second equation for plan B is the one you can use.
assuming you will be using more than 40 minutes per month. the cost functions for both plans becomes:
18.50 per month for plan A.
2.50 per month + .10 per minute for plan B.
if we let x equal the number of minutes, and we let c equal the cost per month, the 2 equations become:
c = 18.50 for plan A.
c = 2.50 + .10 * x for plan B.
plan A will become cheaper when the total cost for plan A is less than the total cost for plan B.
in algebraic terms, this means 18.50 < 2.50 + .10 * x
subtract 2.50 from both sides of this equation to get 18.50 - 2.50 < .10 * x
simplify to get 16.00 < .10 * x
divide both sides of this equation by .10 to get 16.00 / .10 < x
simplify to get 160 < x.
this is the same as x > 160.
plan A will be cheaper when the total minutes of use are greater than 160.
when the total minutes of use are exactly 160, the plans should cost the same.
this would be the break even point.
cost for plan A would be 18.50.
cost for plan B would be 2.50 + .10 * 160 = 2.50 + 16.00 = 18.50
any minutes of use greater than 160 will result in plan A being cheaper.
for example, if 200 minutes of use, then:
plan A costs 18.50
plan B costs 2.50 + .10 * 200 = 2.50 + 20.00 = 22.50.
plan A is cheaper.
note that your cost function for plan B could just as easily have been:
c = 6.50 + .10 * (x-40).
this equation charges 6.50 and then charges 10 cents per minute for all minutes greater than 40.
this equation is equivalent to c = 2.50 + .10 * x.
here's how.
start with c = 6.50 + .10 * (x-40)
simplify to get c = 6.50 + .10 * x - .10 * 40
simplify further to get c = 6.50 + .10 * x - 4.00
simplify further to get c = 2.50 + .10 * x.
you could just have easily started with the cost for plan B shown as c = 6.50 + .10 * (x-40) and the result would have been the same.
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