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?

Let's break down the problem step by step.

### Known information:
1. 30% of the guests drank wine.
2. 54 of the wine drinkers were men.
3. The rest of the wine drinkers were women.
4. 114 women drank beer.
5. The rest of the men drank beer.

### Let the total number of guests be \( G \).

#### Step 1: Wine drinkers
Since 30% of the guests drank wine, the number of wine drinkers is:
\[
0.3 \times G
\]

#### Step 2: Men who drank wine
From the problem, we know that 54 men drank wine. So, the number of women who drank wine is the remaining wine drinkers, given by:
\[
\text{Women wine drinkers} = 0.3G - 54
\]

#### Step 3: Beer drinkers
All other guests drank beer. Thus, the number of beer drinkers is \( 0.7G \) (since 70% drank beer).

- We know that 114 women drank beer, and the rest of the beer drinkers were men. So the number of men who drank beer is:
\[
\text{Men beer drinkers} = 0.7G - 114
\]

#### Step 4: Total men and women
The total number of men is the sum of men who drank wine and men who drank beer:
\[
\text{Total men} = 54 + (0.7G - 114) = 0.7G - 60
\]

The total number of women is the sum of women who drank wine and women who drank beer:
\[
\text{Total women} = (0.3G - 54) + 114 = 0.3G + 60
\]

Since the total number of guests \( G \) is the sum of the total number of men and women, we have:
\[
\text{Total guests} = (0.7G - 60) + (0.3G + 60) = G
\]

This simplifies to \( G = G \), which is trivially true, but doesn't directly tell us \( G \). However, we can use this system of equations to see that it is internally consistent.

#### Step 5: Solving for the number of women who drank wine
From earlier:
\[
\text{Women wine drinkers} = 0.3G - 54
\]

Thus, the number of women who drank wine depends on the total number of guests \( G \). Since there isn't enough information to find \( G \) exactly from the given details, we'd need an additional piece of information to determine the precise number of women wine drinkers.

However, based on the system we've set up, the expression for the number of women wine drinkers is \( 0.3G - 54 \). Let me know if there's more information to use, or if you'd like to explore a different aspect of this problem.

---

Would you like to discuss further details or ask for clarification? Here are some follow-up questions you might want to consider:

1. How would the result change if the total number of guests was provided?
2. Can we determine the ratio of men to women at the party?
3. What assumptions can we make if the problem is incomplete?
4. How would the answer differ if 40% of the guests drank wine instead?
5. Can you figure out the total number of men and women at the party?

**Tip:** Always ensure that the problem provides enough information before solving; if something feels missing, there may be an assumption to explore.

Solve the problem where 30% of the guests at a party drank wine, and 54 of them were men. Learn how to calculate how many women drank wine and break down the problem using percentage and algebraic equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation