Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 1 - Problem Solving and Critical Thinking - 1.3 Problem Solving - Exercise Set 1.3: 69


A – 4 seats B – 6 seats C – 8 seats D – 12 seats

Work Step by Step

The populations, in thousands, are: A – 275 B – 383 C – 465 D – 767 Total – 1890 The total number of seats is 30. Since we're assigning seats according to population, we can calculate how many thousands of people should equate to one seat. $1890\div30=63$ thousands of people. With that in mind, the states should have: A - $275\div63\approx4.37 seats$ B - $383\div63\approx6.08 seats$ C - $465\div63\approx7.38 seats$ D - $767\div63\approx12.17 seats$ However, we need whole numbers, so when we round down, we have: A – 4 seats B – 6 seats C – 7 seats D – 12 seats We have $30-12-7-6-4=1$ seat left. It would be fair to give it to the state which has the highest value after the decimal point, as that state's people becomes the least influential as a result of the rounding down. This gives state C another seat. The final allocation of seats is: A – 4 seats B – 6 seats C – 8 seats D – 12 seats
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