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Math Help - linear relationships?

  1. #1
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    linear relationships?

    Hey guys I'm new here, hoping to get to know you guys . Anyways i have this linear problem thats been doing my head in and there is no answer for it.

    Hussein has just gained his real estate licence and is about to commence work for Hacking real estate agency. Hussein inquires about the cost of a mobile phone with two major phone companies optra and teltus.

    Teltus has a billing system where the monthly cost can be middles by the equation Ct= 0.3x+15.
    Optra believes that a majorit of customers make between 60 and 80 calls per month.
    If optra charges a flat fee of $12 per month, how much should they charge per call (m) as to attract the majorit of customers ?

    I got 0.3<m>0.3375 (m is bigger, not including 30, and smaller than, not including 0.3375. I don't know if I got the signs right). It can't be 0.3 otherwise it'll be cheaper no matter what and it can't be 0.3375 because it'll cost the same for 80 calls.

    For some reason i dont think its right but it makes sense yeah? thank you
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  2. #2
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    Re: linear relationships?

    Your wording makes the question a bit hard to understand (middles?) but if Optra wants to be cheaper than Teltus across the interval of (60,80) calls then you can, as you did, solve for

    $$0.3(80)+15=80m+12 \Rightarrow m=0.3375$$

    Looking at the graph below you can see that using a cost of $0.3375 per call keeps Optra cheaper than Teltus across the entire call range of interest. If they charge more than this they become more expensive than Teltus towards the higher end of the range.

    linear relationships?-clipboard01.jpg
    Thanks from mash
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  3. #3
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    Re: linear relationships?

    I'm sorry, modelled. That's the thing though, it doesn't really say. It wants to attract a majority so of course it has to be cheaper than 'teltus' but it theory it could be lower than 0.3375 . Thanks for the quick reply
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