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Difficulty: MediumPercents and Percent Change

A technology company monitored the annual carbon emissions of its data centers. In 2025, the data centers' carbon emissions decreased by 12%12\% compared to the emissions in 2024. In 2026, the emissions were 387.2387.2 metric tons, which represented a 10%10\% increase compared to the emissions in 2025. What were the data centers' carbon emissions, in metric tons, in 2024?

  1. A
    380
  2. B
    394
  3. C
    396
  4. 400Answer

Answer

400
The correct answer is 400. To find the carbon emissions in 2024, we can set up the relationship using the variable EE for the 2024 emissions. A 12%12\% decrease in 2025 means the emissions were 0.88E0.88E. A 10%10\% increase in 2026 means the emissions were 1.10×0.88E=0.968E1.10 \times 0.88E = 0.968E. Since the 2026 emissions were 387.2387.2 metric tons, we solve 0.968E=387.20.968E = 387.2 to get E=400E = 400.

Step-by-Step Solution

1
Set up an equation for the 2025 emissions in terms of the 2024 emissions (EE).
2025 emissions=E×(1−0.12)=0.88E2025\text{ emissions} = E \times (1 - 0.12) = 0.88E
The emissions in 2025 decreased by 12%12\% compared to the emissions in 2024.
2
Set up an equation for the 2026 emissions in terms of the 2025 emissions.
2026 emissions=2025 emissions×(1+0.10)=1.10×0.88E=0.968E2026\text{ emissions} = 2025\text{ emissions} \times (1 + 0.10) = 1.10 \times 0.88E = 0.968E
The emissions in 2026 represented a 10%10\% increase compared to the emissions in 2025.
3
Equate the expression for 2026 emissions to the given value and solve for EE.
0.968E=387.2  ⟹  E=387.20.968=4000.968E = 387.2 \implies E = \frac{387.2}{0.968} = 400
The 2026 emissions are given as 387.2387.2 metric tons.

Key Concept

Solving multi-step percent change problems by working backward using the correct base values.

Alternative Method

Instead of setting up an algebraic equation, we can work backward step-by-step. First, find the 2025 emissions by reversing the 10%10\% increase from 2025 to 2026: 387.21.10=352\frac{387.2}{1.10} = 352 metric tons. Next, find the 2024 emissions by reversing the 12%12\% decrease from 2024 to 2025: 3520.88=400\frac{352}{0.88} = 400 metric tons.
Estimated Time:1m 15s
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Topics

Percents and Percent Change

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