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The Problem

According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?

Answer provided by our tutors

let

t = the number of years, counting from 2000, needed to have equal populations

C(t) = 7720 + 80t is the number of people in Canton t years after 2000

S(t) = 3200 + 120t is the number of people in Holly Springs t years after 2000

C(t) = S(t)

7720 + 80t = 3200 + 120t give the value for t counting from 2000 before the populations are equal

120t - 80t = 7720 - 3200

40t = 4520

t = 4520/40

t = 113

since now we are 2013 and 2013 - 2000 = 13 there will be 113 - 13 = 100 years before the populations are equal.

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