Calculate 35 Percent of 1000 Liters: Pool Water Reduction Problem

Q: Why do I convert 35% to 0.35?

Percent means "per hundred", so 35% = $ \frac{35}{100} $ = 0.35. Converting to decimal form makes multiplication much easier!

Q: How do I know if I should find what remains or what's gone?

Read the question carefully! This problem says "35% remains" and asks "how many liters are left" - both point to finding the remaining amount, not the lost amount.

Q: What if the percentage was bigger, like 120%?

Percentages over 100% mean the final amount is larger than the original. For example, 120% of 1000 would be 1200 liters - an increase of 200 liters.

Q: Can I solve this without using decimals?

Yes! You can use fractions: $ \frac{35}{100} \times 1000 = \frac{35000}{100} = 350 $. Both methods give the same answer.

Q: How do I check if 350 liters makes sense?

Think logically: 35% is about one-third, so the answer should be roughly 1000 ÷ 3 ≈ 333. Since 350 is close to 333, our answer makes sense!

Percentage Calculations with Real-World Applications

A pool contains 1000 liters of water. After three days, 35% of the total water remains. How many liters are left in the pool after three days?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A pool contains 1000 liters of water. After three days, 35% of the total water remains. How many liters are left in the pool after three days?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the percentage of the initial amount needed.
Step 2: Calculate the corresponding amount of water using the percentage formula.

Now, let's work through each step:

Step 1: We need to find 35% of the initial 1000 liters.

Step 2: Using the formula to find a percentage of a number, we have:

\text{Amount of water remaining} = \left(\frac{35}{100}\right) \times 1000

Calculating this gives:

= 0.35 \times 1000

= 350

Therefore, the number of liters left in the pool after three days is $350$ liters.

Final Answer

350

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage × Original Amount = Final Amount
Technique: Convert 35% to 0.35, then multiply: 0.35 × 1000
Check: Final amount should be less than original: 350 < 1000 ✓

Common Mistakes

Avoid these frequent errors

Finding the amount lost instead of amount remaining
Don't calculate 65% (the amount lost) when asked for remaining water = 650 liters wrong answer! The problem asks for what remains, not what's gone. Always read carefully: 35% remains means multiply by 0.35.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

Why do I convert 35% to 0.35?

Percent means "per hundred", so 35% = $\frac{35}{100}$ = 0.35. Converting to decimal form makes multiplication much easier!

How do I know if I should find what remains or what's gone?

Read the question carefully! This problem says "35% remains" and asks "how many liters are left" - both point to finding the remaining amount, not the lost amount.

What if the percentage was bigger, like 120%?

Percentages over 100% mean the final amount is larger than the original. For example, 120% of 1000 would be 1200 liters - an increase of 200 liters.

Can I solve this without using decimals?

Yes! You can use fractions: $\frac{35}{100} \times 1000 = \frac{35000}{100} = 350$ . Both methods give the same answer.

How do I check if 350 liters makes sense?

Think logically: 35% is about one-third, so the answer should be roughly 1000 ÷ 3 ≈ 333. Since 350 is close to 333, our answer makes sense!

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