# General Equations - Word Problem

• January 26th 2013, 02:56 PM
Sprinkledozer
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
• January 26th 2013, 04:49 PM
Soroban
Re: General Equations - Word Problem
Hello, Sprinkledozer!

Quote:

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