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proportion problem people ratio

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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!