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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- Jan 26th 2013, 02:56 PMSprinkledozerGeneral 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

- Jan 26th 2013, 04:49 PMSorobanRe: 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 $\displaystyle P_1$ and $\displaystyle P_2$ that are $\displaystyle d$ miles apart is given by:

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

115. Estimate the population $\displaystyle (P_1)$ of a city given that

. . . . . the population of a second city is: $\displaystyle P_2 = 48,\!000$,

. . . . . the number of phone calls per day is: $\displaystyle N = 1,\!100,\!000$,

. . . . . and the distance between the cities is: $\displaystyle d=75$ miles.

. . . Round to the nearest thousand.

First, solve for $\displaystyle P_1.$

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

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

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

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

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