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Zorluk: OrtaPercents and Percent Change

An organic farm harvested a certain amount of wheat in 2024. In 2025, due to favorable weather, the amount of wheat harvested was 25%25\% greater than in 2024. In 2026, due to a dry season, the harvest was 12%12\% less than in 2025. If the farm harvested 880880 bags of wheat in 2026, how many bags of wheat did it harvest in 2024?

Cevap: 800 bags

Cevap

800
The correct answer is 800. Let the 2024 harvest be ww bags. A 25%25\% increase in 2025 means the harvest became 1.25w1.25w. A subsequent 12%12\% decrease in 2026 means the harvest became 0.880.88 of the 2025 value, which is 1.25w×0.88=1.1w1.25w \times 0.88 = 1.1w. Given that the 2026 harvest was 880880 bags, we solve 1.1w=8801.1w = 880 to find w=800w = 800.

Adım Adım Çözüm

1
Define the variable for the 2024 harvest and write an expression for the 2025 harvest.
The harvest in 2025 is 1.25w1.25w, where ww is the harvest in 2024.
An increase of 25% is equivalent to multiplying the original value by 1+0.25=1.251 + 0.25 = 1.25.
2
Write an expression for the 2026 harvest in terms of the 2024 harvest variable.
The harvest in 2026 is 1.1w1.1w.
A decrease of 12% is equivalent to multiplying the 2025 value by 1−0.12=0.881 - 0.12 = 0.88. Multiplying the factors gives 1.25×0.88=1.11.25 \times 0.88 = 1.1.
3
Set up an equation using the 2026 harvest total of 880 and solve for the 2024 harvest variable.
w=800w = 800
Dividing the 2026 harvest value of 880 by the cumulative rate of 1.1 yields the initial 2024 value.

Anahtar Kavram

Solving for initial values in multi-step percent change scenarios.

Alternatif Yöntem

Work backward from the final year. The 2026 harvest of 880880 bags is 12%12\% less than the 2025 harvest, meaning it represents 88%88\% of the 2025 harvest. Thus, the 2025 harvest was 880/0.88=1000880 / 0.88 = 1000 bags. The 2025 harvest of 10001000 bags was 25%25\% greater than the 2024 harvest, meaning it represents 125%125\% of the 2024 harvest. Thus, the 2024 harvest was 1000/1.25=8001000 / 1.25 = 800 bags.
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Percents and Percent Change

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