At a party, 30% of the guests drank wine. 54 of the wine-drinkers were men. The remaining of the wine-drinkers were women. 114 women and the rest of the men drank beer. How many wine drinkers were women? b) what fraction of guests were men who took beer?

Let's break this problem into parts:

### Part A: How many wine drinkers were women?

1. Let's assume the total number of guests at the party is \( G \).
2. From the problem, we know that 30% of the guests drank wine, meaning that:
   \[
   0.3G \text{ drank wine}.
   \]
3. Out of the wine drinkers, 54 were men. Thus, the number of women who drank wine is:
   \[
   \text{Women wine drinkers} = 0.3G - 54.
   \]

### Part B: What fraction of guests were men who drank beer?

1. It is given that 114 women and the remaining men drank beer. The number of men who drank beer can be found by subtracting the men who drank wine from the total number of men. 
   
2. Let's assume that the number of men at the party is \( M \) and the number of women is \( W \). Therefore:
   \[
   G = M + W.
   \]
3. The number of men who drank beer is \( M - 54 \) since 54 men drank wine.

Thus, the fraction of guests who were men that drank beer is:
\[
\frac{M - 54}{G}.
\]

### Conclusion:
- To find the number of women wine drinkers in Part A, we need the total number of guests \( G \), but we can express the number of women wine drinkers as \( 0.3G - 54 \).
- The fraction of men who drank beer in Part B is \( \frac{M - 54}{G} \), where \( M \) is the total number of men and \( G \) is the total number of guests.

Do you have information on the total number of guests? Or would you like further details?

### 5 Related Questions:
1. How do you calculate the total number of guests if the number of women and men drinking beer is known?
2. How can we express the number of women who drank beer mathematically?
3. What is the relationship between men who drank beer and total male guests?
4. If 70% of the guests drank beer, how can we find the total number of guests?
5. How would the problem change if 40% of the guests drank wine instead?

**Tip**: Always verify the total number of guests in problems involving percentages to avoid ambiguity.

At a party, 30% of the guests drank wine. 54 of the wine-drinkers were men. The remaining of the wine-drinkers were women. 114 women and the rest of the men drank beer. How many wine drinkers were women? b) What fraction of guests were men who took beer?

This problem helps students solve a real-world scenario using percentages and algebra. Learn how to calculate the number of women who drank wine and the fraction of men who drank beer, given that 30% of guests drank wine and 114 women drank beer. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation