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Zorluk: OrtaPercents and Percent Change

In 2024, a city recycled a certain number of tons of plastic. In 2025, the number of tons of plastic recycled was 15%15\% greater than the number of tons recycled in 2024. In 2026, the number of tons of plastic recycled was 20%20\% less than the number of tons recycled in 2025. If the city recycled 5,5205,520 tons of plastic in 2026, how many tons of plastic did the city recycle in 2024?

Cevap: 6000

Cevap

The city recycled 6,0006,000 tons of plastic in 2024.
To find the number of tons of plastic recycled in 2024, we must work backward from the 2026 value of 5,520 tons. Let xx represent the tons recycled in 2025. Since the 2026 value represents a 20%20\% decrease from 2025, we have 0.80x=5,5200.80x = 5,520, which simplifies to x=6,900x = 6,900 tons. Next, let yy represent the tons recycled in 2024. Since the 2025 value represents a 15%15\% increase from 2024, we have 1.15y=6,9001.15y = 6,900. Solving for yy yields y=6,9001.15=6,000y = \frac{6,900}{1.15} = 6,000 tons.

Adım Adım Çözüm

1
Set up an equation to find the amount of plastic recycled in 2025 using the 2026 amount of 5,520 tons.
The amount of plastic recycled in 2025 was 6,9006,900 tons.
The 2026 amount is a 20%20\% decrease from the 2025 amount, so 5,5205,520 is equal to 80%80\% of the 2025 amount. Solving 0.80x=5,5200.80x = 5,520 gives x=6,900x = 6,900.
2
Set up an equation to find the amount of plastic recycled in 2024 using the 2025 amount of 6,900 tons.
The amount of plastic recycled in 2024 was 6,0006,000 tons.
The 2025 amount is a 15%15\% increase from the 2024 amount, so 6,9006,900 is equal to 115%115\% of the 2024 amount. Solving 1.15y=6,9001.15y = 6,900 gives y=6,000y = 6,000.

Anahtar Kavram

Working backward through multiple sequential percentage changes.
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Konular

Percents and Percent Change

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