SAT Ratios, rates, proportional relationships, and units Practice Question 10 (Hard)

Question bank / Ratios, rates, proportional relationships, and units

Math · Problem-Solving and Data AnalysisHard

County A has an area of $1{,}240$ square miles and a population density of $85$ people per square mile. County B has an area of $760$ square miles and a population of $120{,}600$ people. What is the population density, in people per square mile, of the two counties combined?

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Answer: 113

County A's population is $1{,}240 \times 85 = 105{,}400$ . The combined population is $105{,}400 + 120{,}600 = 226{,}000$ , and the combined area is $1{,}240 + 760 = 2{,}000$ square miles. The combined density is $\frac{226000}{2000} = 113$ people per square mile.

Averaging the two densities ( $85$ and about $158.7$ ) gives about $121.8$ , which ignores that the counties have different areas.

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