Examkin

Question

Difficulty: MediumPercents and Percent Change

In 2024, a solar power system generated 250250 megawatt-hours of electricity. In 2025, the system's electricity generation was 12%12\% greater than in 2024. In 2026, the electricity generation was 5%5\% less than in 2025. How many megawatt-hours of electricity did the solar power system generate in 2026?

Answer: 266 megawatt-hours

Answer

266
To find the electricity generation in 2026, we first determine the generation in 2025. Since the 2025 generation was 12%12\% greater than the 2024 generation of 250250 megawatt-hours, the 2025 generation is 250×(1+0.12)=250×1.12=280250 \times (1 + 0.12) = 250 \times 1.12 = 280 megawatt-hours. Next, the 2026 generation was 5%5\% less than the 2025 generation of 280280 megawatt-hours. Therefore, the 2026 generation is 280×(1−0.05)=280×0.95=266280 \times (1 - 0.05) = 280 \times 0.95 = 266 megawatt-hours.

Step-by-Step Solution

1
Calculate the electricity generation in 2025.
280 megawatt-hours
The 2025 generation is 12%12\% greater than the 2024 generation of 250250 megawatt-hours. So, we multiply 250250 by 1+0.12=1.121 + 0.12 = 1.12 to get 280280.
2
Calculate the electricity generation in 2026.
266 megawatt-hours
The 2026 generation is 5%5\% less than the 2025 generation of 280280 megawatt-hours. So, we multiply 280280 by 1−0.05=0.951 - 0.05 = 0.95 to get 266266.

Key Concept

Calculating consecutive percent changes by applying each percentage change to the correct sequential base value.

Alternative Method

We can set up a single equation representing the sequential changes: 2026 Generation=250×(1+0.12)×(1−0.05)=250×1.12×0.95=266\text{2026 Generation} = 250 \times (1 + 0.12) \times (1 - 0.05) = 250 \times 1.12 \times 0.95 = 266 megawatt-hours.
Estimated Time:1m 15s
Rate this question

Topics

Percents and Percent Change

More questions from this topic