At the beginning of 2014, the number of lions in the park was p percent of the total number of large animals. Which of the following is closest to the value of p?
Understand the Problem
The question is asking us to determine the percentage of lions in a park in relation to the total number of large animals. It's specifically asking for the closest value of 'p', which represents the percentage of lions compared to the total animal count.
Answer
The value of $p$ is 2.
Answer for screen readers
The closest value of $p$ is 2.
Steps to Solve
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Understanding the equation
The problem states that the number of lions is $p%$ of the total number of large animals. To express this mathematically, we can write the equation:
$$ \text{number of lions} = \frac{p}{100} \times \text{total number of large animals} $$
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Identifying the values
From the information given, we can assume that the number of lions is 200. Therefore, substituting in our equation gives us:
$$ 200 = \frac{p}{100} \times 10000 $$
where 10,000 is the total number of large animals.
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Solving for p
Rearranging the equation to solve for $p$, we multiply both sides by 100:
$$ 200 \times 100 = p \times 10000 $$
This simplifies to:
$$ 20000 = p \times 10000 $$
Now, divide both sides by 10,000:
$$ p = \frac{20000}{10000} $$
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Calculating p
Carrying out the division gives:
$$ p = 2 $$
The closest value of $p$ is 2.
More Information
In this scenario, we determined that the number of lions in the park accounted for 2% of the total number of large animals, which was 10,000. Using basic percentage calculations, we found that 2% reflects the corresponding count of lions as 200.
Tips
- Misunderstanding percentages: Sometimes, people may confuse the percentage with the actual number. It's important to always clarify what is being asked (the percentage vs. the amount).
- Arithmetic errors: Mistakes in basic arithmetic during multiplicative or divisive calculations can lead to incorrect answers. Double-check calculations to ensure accuracy.
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