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Difficulty: MediumPercents and Percent Change

In 2015, the population of a certain species of owl in a nature reserve was xx. By 2020, the population had increased by 35%35\%. Between 2020 and 2025, the population decreased by 20%20\% of its 2020 value. If the population of the owl species in 2025 was 270270, what was the value of xx?

Answer: 250

Answer

The population in 2015 was 250.
To find the initial population xx, we apply the percent changes sequentially. A 35%35\% increase is represented by multiplying by 1.351.35, and a 20%20\% decrease is represented by multiplying by 0.800.80. The final population in terms of xx is x×1.35×0.80=1.08xx \times 1.35 \times 0.80 = 1.08x. Given that the population in 2025 is 270270, we set up the equation 1.08x=2701.08x = 270. Dividing both sides by 1.081.08 yields x=250x = 250.

Step-by-Step Solution

1
Write an expression for the owl population in 2020 in terms of xx.
The population in 2020 was 1.35x1.35x.
An increase of 35%35\% is represented by multiplying the initial amount by 1+0.35=1.351 + 0.35 = 1.35.
2
Write an expression for the owl population in 2025 in terms of xx.
The population in 2025 was 1.08x1.08x.
A decrease of 20%20\% from the 2020 population is represented by multiplying the 2020 population by 1−0.20=0.801 - 0.20 = 0.80. Thus, the 2025 population is 1.35x×0.80=1.08x1.35x \times 0.80 = 1.08x.
3
Set the expression for the 2025 population equal to the given value of 270 and solve for xx.
x=250x = 250
Solving the equation 1.08x=2701.08x = 270 by dividing both sides by 1.081.08 gives x=2701.08=250x = \frac{270}{1.08} = 250.

Key Concept

Consecutive percent changes
Estimated Time:1m 30s
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Topics

Percents and Percent Change

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