Calculate Black Chairs: Finding 40 Percent of 125 Using Complementary Percentages

Q: Why can't I just use 60% to find the black chairs?

Because 60% represents the white chairs, not the black ones! The black chairs make up the remaining 40% since 100% - 60% = 40%.

Q: How do I know what percentage the black chairs represent?

Use the fact that all percentages must add to 100%. If white chairs are 60%, then black chairs must be 100% - 60% = 40%.

Q: What if the percentages don't add up to 100%?

Check your work! In complete groups like "all chairs in a room," the percentages of all parts must total exactly 100%. If they don't, there's an error in the problem or your calculation.

Q: Can I solve this without using decimals?

Absolutely! Convert to fractions: 60% = $\frac{3}{5}$, so white chairs = $\frac{3}{5} \times 125 = 75$. Then 125 - 75 = 50 black chairs.

Complementary Percentages with Subtraction Method

There are 125 chairs in a room. 60% of the chairs are white , while the rest are black. How many black chairs are there?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the number of black chairs

00:05 Subtract the percentage of white chairs from the whole in order to determine the percentage of blacks

00:15 This is the percentage of black chairs

00:20 Use the formula to convert percentages to fractions

00:26 Apply this formula to our exercise

00:31 Multiply this fraction by the whole in order to identify the total number of black chairs

00:46 Break down 40 into factors of 4 and 10, and 125 into factors of 25 and 5

00:51 Break down 100 into factors of 25 and 4

01:01 Reduce wherever possible

01:10 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There are 125 chairs in a room. 60% of the chairs are white , while the rest are black. How many black chairs are there?

Step-by-step solution

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

Step 1: Calculate the number of white chairs from the given percentage.
Step 2: Determine the number of black chairs by subtraction.

Let's work through each step:

Step 1: Calculate the number of white chairs.
The total number of chairs is 125. Since 60% of these chairs are white, we calculate the number of white chairs as follows:
$\text{White chairs} = 125 \times 0.60 = 75$

Step 2: Determine the number of black chairs.
Subtract the number of white chairs from the total number of chairs to find the number of black chairs:
$\text{Black chairs} = 125 - 75 = 50$

Therefore, the number of black chairs is 50.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Total percentage always equals 100% for all items combined
Technique: Find 40% directly: $125 \times 0.40 = 50$
Check: White chairs (75) + Black chairs (50) = 125 total ✓

Common Mistakes

Avoid these frequent errors

Calculating 60% instead of 40% for black chairs
Don't calculate 125 × 0.60 = 75 black chairs! This gives you the white chairs instead. Always identify which percentage represents your target group - black chairs are the remaining 40%, not 60%.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just use 60% to find the black chairs?

Because 60% represents the white chairs, not the black ones! The black chairs make up the remaining 40% since 100% - 60% = 40%.

Is there a faster way than subtracting from the total?

Yes! Since black chairs are 40% of the total, calculate directly: $125 \times 0.40 = 50$ . Both methods give the same answer.

How do I know what percentage the black chairs represent?

Use the fact that all percentages must add to 100%. If white chairs are 60%, then black chairs must be 100% - 60% = 40%.

What if the percentages don't add up to 100%?

Check your work! In complete groups like "all chairs in a room," the percentages of all parts must total exactly 100%. If they don't, there's an error in the problem or your calculation.

Can I solve this without using decimals?

Absolutely! Convert to fractions: 60% = $\frac{3}{5}$ , so white chairs = $\frac{3}{5} \times 125 = 75$ . Then 125 - 75 = 50 black chairs.

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