Explanation Given Information: The number of phone calls were made between two cities is 80,000, which are 400 mi apart with populations of 70 , 000 and 100 , 000 . The number of long-distance phone calls between two cities varies jointly as the population of the two cities and varies inversely as the distance between them. Formula used: Ifone variable y varies directly as one variable x and inversely as another variable z , then by definition of combined variation, there exists a real number k such that, y = k x z Calculation: There are 80,000 phone calls were made between two cities, which are 400 mi apart with populations of 70 , 000 and 100 , 000 . The number of long-distance phone calls made between the two cities which are at a distance of 250 mi apart with populations of 50 , 000 and 75 , 000 is calculated as, Firstly, define the variables as, n = number of phone-calls p 1 = population of city 1 p 2 = population of city 2 d = distance between the two cities Frame the variation equation, The number of long-distance phone calls between two cities varies jointly as the population of the two cities and varies inversely as the distance between them, by the definition of combined variation, the variation equation is, n = k p 1 p 2 d Here, k is the constant of variation. To find the value of the constant of variation, use the provided information that 80 , 000 phone calls were made between two cities which are 400 mi apart with populations of 70 , 000 and 100 , 000 . Substitute n = 80 , 000 , p 1 = 70 , 000 , p 2 = 100 , 000 and d = 400 in n = p 1 p 2 d . 80 , 000 = k ( 70 , 000 ) ( 100 , 000 ) 400 Multiply. So, 80 , 000 = 7000000000 k 400 Multiply by 400 and divide by 7000000000 on both the sides of the equation

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 9.4, Problem 65E

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To calculate: The number of long-distance phone calls made between the two cities which are at a distance of 250 mi apart with populations of 50,000 and 75,000.

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Chapter 9.4, Problem 64E

Chapter 9.4, Problem 66E

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Beginning and Intermediate Algebra (6th Edition)

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The number of long-distance phone calls made between the two cities which are at a distance of 250 mi apart with populations of 50 , 000 and 75 , 000 .

Solution Summary: The author calculates the number of long-distance phone calls made between two cities, which are at a distance of 250mi apart.

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To calculate: The number of long-distance phone calls made between the two cities which are at a distance of 250 mi apart with populations of 50,000 and 75,000.

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