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My textbook had this question: There are 2 companies working in city A: Newton a

ID: 1249740 • Letter: M

Question

My textbook had this question:

There are 2 companies working in city A: Newton and Garfield

Newton exports all their products outside the city and Garfield only sells their products within the city. Newton experiences growth, so it hires 100 more workers, all of whom come to reside in city A. Because of this, Garfield - at the first stage - hires 60 more workers.

From these facts, and working under the assumption that every additional stage of growth will cause a rise of 60 percent to the number of workers that were added in the previous stage, what is the total number of workers that will be added to city A?

The answer given in the book is 250, of which 150 will be absorbed by Garfield.

Please explain how they arrived at this answer. Thank you

Explanation / Answer

Total no. of workers = workers added by Newton + workers added in several stages by Garfield = 100 + 60(1+ 0.6 + 0.6^2 +...+0.6^(n -1)) where n tends to infinity. (second term in bracket is in Geometric Progression with common ratio of 0.6) = 100 +60 (1 - 0.6^n)/(1 - 0.6) = 100 + 60 * 1/0.4 (since 0.6^n = 0 as n tends to infinity) = 100 + 150 = 250 (ANSWER)