## Thinking Mathematically (6th Edition)

(a) We can find the standard divisor. $standard~divisor = \frac{total ~population}{number~of~ items}$ $standard~divisor = \frac{1600}{200}$ $standard~divisor = 8$ The standard divisor is 8 (thousand). There are 8,000 people for each seat in congress. (b) We can find each state's standard quota. The standard quota of each state is the state's population divided by the standard divisor. State A: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{138}{8}$ $standard~quota = 17.25$ State A's standard quota is 17.25 State B: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{266}{8}$ $standard~quota = 33.25$ State B's standard quota is 33.25 State C: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{534}{8}$ $standard~quota = 66.75$ State C's standard quota is 66.75 State D: $standard ~quota = \frac{population}{standard~divisor}$ $standard~quota = \frac{662}{8}$ $standard~quota = 82.75$ State D's standard quota is 82.75 (c) The lower quota is the standard quota rounded down to the nearest whole number. The upper quota is the standard quota rounded up to the nearest whole number. We can find each state's lower quota and upper quota. State A's standard quota is 17.25 State A's lower quota is 17 State A's upper quota is 18 State B's standard quota is 33.25 State B's lower quota is 33 State B's upper quota is 34 State C's standard quota is 66.75 State C's lower quota is 66 State C's upper quota is 67 State D's standard quota is 82.75 State D's lower quota is 82 State D's upper quota is 83