Question

proportion problem people ratio

Answer 1

Sure! Proportion problems involving ratios often have to do with comparing quantities. Let's go through an example and how to solve it.

### Example Problem:
Let's say you have a class with boys and girls. The ratio of boys to girls is 3:2. If there are 15 boys in the class, how many girls are there?

### Solution:
1. **Understand the Ratio**:
The ratio of boys to girls is 3:2. This means that for every 3 boys, there are 2 girls.

2. **Set up the Ratios**:
Let the number of boys be represented as \(3x\) and the number of girls as \(2x\), where \(x\) is a common factor.

3. **Use the Given Information**:
According to the problem, the number of boys is 15. So, we set up the equation:
\[
3x = 15
\]

4. **Solve for \(x\)**:
Divide both sides by 3:
\[
x = 5
\]

5. **Find the Number of Girls**:
Now substitute \(x\) back into the expression for the number of girls:
\[
2x = 2(5) = 10
\]

### Answer:
There are 10 girls in the class.

### Example Problem 2:
If the total number of people is 100 and the ratio of men to women is 4:1, how many men and women are there?

### Solution:
1. **Understand the Total Ratio**:
The ratio of men to women is 4:1. This means that for every 4 men, there is 1 woman.

2. **Set Up the Ratios**:
Let the number of men be \(4x\) and the number of women be \(1x\).

3. **Total People**:
The total number of people is:
\[
4x + 1x = 100
\]
\[
5x = 100
\]

4. **Solve for \(x\)**:
Divide both sides by 5:
\[
x = 20
\]

5. **Find the Number of Men and Women**:
- Number of men: \(4x = 4(20) = 80\)
- Number of women: \(1x = 1(20) = 20\)

### Answer:
There are 80 men and 20 women in the group.

If you have a specific ratio problem you'd like help with, please provide the details!