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Math Help - Mobile Phone rate plans - HELP!

  1. #1
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    Exclamation Mobile Phone rate plans - HELP!

    Imagine.. A $50 mobile phone plan.

    Mobile calls 10c per 30 seconds.
    Land Line calls 29c per 30 seconds.

    A customer states "30% of my calls are to mobiles, the other 70% are to landlines, how many hours of talk time (in decimal) do I get for mobile calls and landline calls?"

    I need an equation for this to which I could apply if the percentages changed to say 15% and 85%.

    Thanks guys

    Psylencer.

    By the way I need a response I can understand...Im no maths genius. Thanks
    Last edited by psylencer; June 27th 2006 at 03:16 AM.
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  2. #2
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    Lexington, MA (USA)
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    Hello, psylencer!

    Not to worry . . . Baby-talk is my specialty.


    Imagine.. A $50 mobile phone plan.

    Mobile calls: 10 per 30 seconds.
    Land Line calls: 29 per 30 seconds.

    A customer states "30% of my calls are to mobiles, the other 70% are to landlines.
    How many hours of talk time (in decimal) do I get for mobile calls and landline calls?"

    I need an equation for this to which I could apply if the percentages changed to, say, 15% and 85%.

    Let's solve this particular problem first . . . then we'll generalize it.

    Let T = total talk time (in hours).

    The rates are: \begin{array}{cc}\text{Mobile: \$12/hour} \\ \text{Land: \$34.80/hour}\end{array}

    Since 30% of the calls are Mobile, he talks 0.3T hours at $12/hour.
    . . His mobile calls cost him: (0.3T)(12) = 3.6T dollars.

    Since 70% of the calls are Landline, he talks 0.7T hours at $38.40/hour.
    . . His landline calls cost him: (0.7T)(38.40) = 24.36T dollars.

    His total cost will be $50: . 3.6T + 24.36T\;=\:50

    Solve for T:\;\;27.96T = 50\quad\Rightarrow\quad\boxed{T = 1.788268956\text{ hours.}}

    For his $50, he can talk a total of: \text{1 hour, 47 minutes, 17 seconds}

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Now, we'll generalize the problem,
    . . keeping the hourly rates constant.

    Let p = percent of T used on Mobile calls.
    . . Time on mobile calls: pT hours.
    Then mobile calls cost: pT \times 12 = 12pT dollars.


    Then 1 - p = percent of T used on Landline calls.
    . . Time on landline calls: (1-p)T hours.
    Then landline calls cost: (1-p)T \times 38.4 = 38.4T - 38.4pT dollars.

    The total cost is $50, so: . 12pT + (38.4T - 38.4pT) \:=\:50

    Solve for T and we get: . \boxed{T \:= \:\frac{50}{34.8 - 22.8p}\text{ hours.}}

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  3. #3
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    Smile

    Thanks Soroban,

    I got the first part, but not the last part. As you can probably tell, Im interested in maths (not a student) but no good at it. Any chance we could go back a step? I still dont see how the percentages work. HOLD ON!...I GOT IT..HAHA! Dont worry Thanks heaps. You guys are brilliant.



    Thanks
    Psylencer
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