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Math Help - General Equations - Word Problem

  1. #1
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    General Equations - Word Problem

    Could someone help me figure this out please? I have attached the problem (jpg). If you would like to know the answer lmk. Thanks
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  2. #2
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    Re: General Equations - Word Problem

    Hello, Sprinkledozer!

    A telephone company estimates that the number N of phone calls per day
    between two cities of population P_1 and P_2 that are d miles apart is given by:

    . . N \:=\:\frac{2.51P_1P_2}{d^2}

    115. Estimate the population (P_1) of a city given that
    . . . . . the population of a second city is: P_2 = 48,\!000,
    . . . . . the number of phone calls per day is: N = 1,\!100,\!000,
    . . . . . and the distance between the cities is: d=75 miles.
    . . . Round to the nearest thousand.

    First, solve for P_1.

    We have: . \frac{2.51P_1P_2}{d^2} \:=\:N

    Multiply by d^2\!:\;\;2.51P_1P_2 \:=\:d^2N

    Divide by 2.51P_2\!:\;\;P_1 \;=\;\frac{d^2N}{2.51P_2}

    Substitute: . P_1 \;=\;\frac{75^2(1,\!100,\!000)}{2.51(48,\!000)} \;=\;51,357.07171

    Therefore: . P_1 \;\approx\;51,\!000
    Thanks from Sprinkledozer
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