Problem 79 - Elementary Algebra Within Reach

Question

Writing You are told that the ratio of men to women in a class is 2 to 1 . Does this information tell you the total number of people in the class? Explain.

Step-by-Step Solution

Answer

No, the given ratio of men to women (2:1) in a class does not tell us the total number of people in the class. It only indicates the comparative ratio, not the exact numbers.

Step 1: Defining Variables

Firstly, assign variables. For instance, let's denote the number of men in the class as 'm' and the number of women as 'w'. We then know that the ratio of men to women is 2 : 1, which suggests that for every 2 men, there is 1 woman in the class. This infers \(m = 2w\).

Step 2: Exploring the Ratio

The ratio tells us that there are twice as many men as there are women, but it doesn't give us the exact number of each. Our relation can be true for many values: for example, if \(w = 10\), then \(m = 20\). If \(w = 100\), then \(m = 200\), and so forth.

Step 3: Conclusion

Based on the information provided, we cannot determine the exact number of people in the class. The ratio only tells us the relation between numbers, not their exact values.