General Equations - Word Problem

**Sprinkledozer** · January 26th 2013, 02:56 PM

Could someone help me figure this out please? I have attached the problem (jpg). If you would like to know the answer lmk. Thanks

**Soroban** · January 26th 2013, 04:49 PM

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: . $P_1 \;\approx\;51,\!000$

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