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11.4 Exercise 5

Avg difficulty 2.5

The Air Force administration wants to distribute 27 aircrafts across six bases based on the number of qualified pilots stationed at those bases. The standard quotas for each base are listed in the table below. Use this information to answer the questions.

Base Standard Quota
(A) Alpha 132.2963≈5.66\frac{13}{2.2963} \approx 5.66 aircraft
(B) Bravo 122.2963≈5.23\frac{12}{2.2963} \approx 5.23 aircraft
(C) Charlie 52.2963≈2.18\frac{5}{2.2963} \approx 2.18 aircraft
(D) Delta 162.2963≈6.97\frac{16}{2.2963} \approx 6.97 aircraft
(E) Echo 72.2963≈3.05\frac{7}{2.2963} \approx 3.05 aircraft
(F) Foxtrot 92.2963≈3.92\frac{9}{2.2963} \approx 3.92 aircraft
  1. Give the lower quota for each Air Force base.
  2. Find the sum of the lower quotas. By how much does this sum fall short of the actual number of aircraft?

OpenStax Contemporary Mathematics, 11.4 Apportionment Methods, exercise 5

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Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.