Calculate 75% of Total Population: Finding Female Count Given 9 Males

Q: Why can't I just multiply 9 by 75% to get the number of women?

Because the 9 men represent 25% of the family, not 75%! You need to find the total first, then calculate 75% of that total to get the number of women.

Q: How do I remember which percentage goes with which group?

Always read carefully! If 75% are women, then the remaining 25% must be men. The percentages of all groups always add up to 100%.

Q: What if the problem gave me the number of women instead of men?

Then you'd set up $ 0.75x = $ (number of women) to find the total, then calculate 25% of the total to find the number of men.

Q: Can I solve this without using decimals?

Yes! Think of it as fractions: if 1/4 of the family are men and there are 9 men, then the whole family is $ 9 \times 4 = 36 $ people.

Q: How do I check if my final answer makes sense?

Add women + men to get the totalCalculate the percentage: women ÷ total × 100This should equal 75% ✓

Percentage Problems with Complementary Groups

In Roberto's family, 75% are women and there are 9 men.

Calculate the number of females in Roberto's family.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the number of women in Roberto's family

00:05 The percentage of women according to the given data

00:10 Subtract this percentage from the whole in order to establish the percentage of males

00:15 This is the percentage of males in the family

00:20 The number of males according to the given data

00:30 Multiply by 3 in order to determine the amount equal to 75 percent

00:45 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In Roberto's family, 75% are women and there are 9 men.

Calculate the number of females in Roberto's family.

Step-by-step solution

To solve this problem, let's begin by understanding the situation:

In Roberto's family, 75% of the members are women, and there are 9 men. We need to determine the number of females in the family.

Step 1: Understand the percentage breakdown.

If 75% of the family are women, then 25% are men. This is because percentages of 100% are divided into parts that represent the whole group.

Step 2: Set up the equation for men.

Since 25% of the family are men and there are 9 men, the equation for the total number of family members, $x$ , based on the men is:

$0.25x = 9$

Step 3: Solve for the total number of family members.

We solve the equation for $x$ :

$x = \frac{9}{0.25} = 36$

This tells us that there are 36 members in the family.

Step 4: Calculate the number of females.

Now, calculate the number of females, which is 75% of the total family:

$\text{Number of females} = 0.75 \times 36 = 27$

Therefore, the number of females in Roberto's family is 27.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Complementary Rule: When 75% are women, then 25% are men
Technique: Set up equation $0.25x = 9$ to find total
Check: Verify 27 women + 9 men = 36 total, and 27/36 = 75% ✓

Common Mistakes

Avoid these frequent errors

Using 75% directly with the number of men
Don't multiply 9 × 0.75 = 6.75 thinking this gives the number of women! This uses the wrong percentage group. Always identify which percentage matches your known quantity first - men are 25%, not 75%.

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 multiply 9 by 75% to get the number of women?

Because the 9 men represent 25% of the family, not 75%! You need to find the total first, then calculate 75% of that total to get the number of women.

How do I remember which percentage goes with which group?

Always read carefully! If 75% are women, then the remaining 25% must be men. The percentages of all groups always add up to 100%.

What if the problem gave me the number of women instead of men?

Then you'd set up $0.75x =$ (number of women) to find the total, then calculate 25% of the total to find the number of men.

Can I solve this without using decimals?

Yes! Think of it as fractions: if 1/4 of the family are men and there are 9 men, then the whole family is $9 \times 4 = 36$ people.

How do I check if my final answer makes sense?

Add women + men to get the total
Calculate the percentage: women ÷ total × 100
This should equal 75% ✓

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