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Zorluk: OrtaPercents and Percent Change

A technology company has two regional offices, Office North and Office South. In 2024, the number of employees at Office North was 25%25\% greater than the number of employees at Office South. In 2025, the number of employees at Office North increased by 20%20\%, and the number of employees at Office South decreased by 10%10\%. If the total number of employees at both offices combined in 2025 was 432432, what was the total number of employees at both offices combined in 2024?

  1. A
    360
  2. 405Cevap
  3. C
    225
  4. D
    450

Cevap

405
Let SS represent the number of employees at Office South in 2024. Because Office North has 25%25\% more employees than Office South in 2024, the count at Office North is 1.25S1.25S. The combined total in 2024 is S+1.25S=2.25SS + 1.25S = 2.25S. In 2025, Office North's staff increases by 20%20\%, making it 1.20×1.25S=1.50S1.20 \times 1.25S = 1.50S. Office South's staff decreases by 10%10\%, making it 0.90S0.90S. The combined total in 2025 is 1.50S+0.90S=2.40S1.50S + 0.90S = 2.40S. Given that the total in 2025 is 432432, we solve the equation 2.40S=4322.40S = 432, which gives S=180S = 180. Substituting S=180S = 180 into the expression for the 2024 total yields 2.25×180=4052.25 \times 180 = 405.

Adım Adım Çözüm

1
Define variables for the number of employees in 2024. Let SS be the number of employees at Office South in 2024. Since Office North had 25%25\% more employees, represent Office North as 1.25S1.25S. Express the total number of employees in 2024 as S+1.25S=2.25SS + 1.25S = 2.25S.
Total employees in 2024 is represented by 2.25S2.25S.
To establish a baseline relationship between the employee counts at the two offices.
2
Express the number of employees in 2025 in terms of SS by applying the percentage changes. Office North's employees increased by 20%20\%, which is 1.20×1.25S=1.50S1.20 \times 1.25S = 1.50S. Office South's employees decreased by 10%10\%, which is 0.90×S=0.90S0.90 \times S = 0.90S. Find the total in 2025 by adding these values: 1.50S+0.90S=2.40S1.50S + 0.90S = 2.40S.
Total employees in 2025 is represented by 2.40S2.40S.
To determine the algebraic expression representing the combined count after the percent changes.
3
Set the algebraic expression for the 2025 total equal to the given value of 432432 and solve for SS.
2.40S=432  ⟹  S=1802.40S = 432 \implies S = 180
To find the baseline number of employees at Office South in 2024.
4
Substitute S=180S = 180 back into the expression for the 2024 total (2.25S2.25S) to calculate the final answer.
2.25×180=4052.25 \times 180 = 405
To calculate the combined total number of employees in 2024.

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Percents and Percent Change
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