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Difficulty: Very hardPercents and Percent Change

The table below shows the total number of registered voters in two districts, District X and District Y, in 2020 and 2024.

District2020 registered voters2024 registered voters
District X10,00010,00015,00015,000
District Y15,00015,00018,00018,000

In 2020, 12%12\% of the registered voters in District X and 24%24\% of the registered voters in District Y were between the ages of 18 and 25. In 2024, 16%16\% of the registered voters in District X and 20%20\% of the registered voters in District Y were between the ages of 18 and 25. From 2020 to 2024, what was the percent increase in the total number of registered voters between the ages of 18 and 25 across both districts combined?

  1. A
    20%
  2. 25%Answer
  3. C
    32%
  4. D
    50%

Answer

The percent increase in the total number of registered voters between the ages of 18 and 25 across both districts combined is 25%.
To find the percent increase in the total number of registered voters between the ages of 18 and 25, we first determine the number of voters in this age group for both years. For 2020, District X had 10,000×0.12=1,20010,000 \times 0.12 = 1,200 voters and District Y had 15,000×0.24=3,60015,000 \times 0.24 = 3,600 voters, giving a combined total of 4,8004,800 voters aged 18-25. For 2024, District X had 15,000×0.16=2,40015,000 \times 0.16 = 2,400 voters and District Y had 18,000×0.20=3,60018,000 \times 0.20 = 3,600 voters, giving a combined total of 6,0006,000 voters aged 18-25. The percent increase is computed by dividing the change in this subpopulation by the initial 2020 value: 6,000−4,8004,800×100%=25%\frac{6,000 - 4,800}{4,800} \times 100\% = 25\%. Therefore, the total number of registered voters in this age group increased by 25%.

Step-by-Step Solution

1
Calculate the number of registered voters aged 18-25 in both districts in 2020.
In District X: 10,000×0.12=1,20010,000 \times 0.12 = 1,200. In District Y: 15,000×0.24=3,60015,000 \times 0.24 = 3,600. Total 2020 voters aged 18-25 = 1,200+3,600=4,8001,200 + 3,600 = 4,800.
To find the overall percent change of the subpopulation, we need to know its initial size in 2020.
2
Calculate the number of registered voters aged 18-25 in both districts in 2024.
In District X: 15,000×0.16=2,40015,000 \times 0.16 = 2,400. In District Y: 18,000×0.20=3,60018,000 \times 0.20 = 3,600. Total 2024 voters aged 18-25 = 2,400+3,600=6,0002,400 + 3,600 = 6,000.
To find the overall percent change of the subpopulation, we need to know its final size in 2024.
3
Calculate the absolute increase in the registered voters aged 18-25.
6,000−4,800=1,2006,000 - 4,800 = 1,200 voters.
The percent change formula requires the difference between the final and initial values.
4
Calculate the percent increase relative to the 2020 initial value.
1,2004,800×100%=25%\frac{1,200}{4,800} \times 100\% = 25\%.
The percent increase is defined as the change divided by the initial value, multiplied by 100 to get a percentage.

Key Concept

Calculating percent change for a combined population by computing the absolute initial and final counts of the subpopulation first, rather than manipulating percent rates directly.
Estimated Time:3m 0s
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Topics

Percents and Percent Change

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