Questions: Rico is the administrator for a small city with a population of 10,587. The city is considering annexing unincorporated land in which 1,120 people live. By what percentage will this increase the population of the city? (Round the nearest tenth.)

Solution Steps

To find the percentage increase in the population of the city, we need to calculate the difference between the new population and the original population, then divide that difference by the original population. Finally, multiply the result by 100 to convert it to a percentage.

The original population of the city is 10,587. After annexing the unincorporated land, the new population becomes: \[ \text{New Population} = 10,587 + 1,120 = 11,707 \]

The increase in population is the difference between the new population and the original population: \[ \text{Population Increase} = 11,707 - 10,587 = 1,120 \]

To find the percentage increase, divide the population increase by the original population and multiply by 100: \[ \text{Percentage Increase} = \left(\frac{1,120}{10,587}\right) \times 100 \approx 10.5790\% \]

Round the percentage increase to the nearest tenth: \[ \text{Rounded Percentage Increase} = 10.6\% \]

Final Answer