https://file.aiquickdraw.com/mathbot/file/1730312201432ehzh1ojx.jpg

Let's solve the problem.

### Step-by-Step Solution:

Let \( N \) represent the total number of guests at the wedding.

1. **Beef:**  
   \( \frac{1}{5} \) of the guests chose beef, so:
   \[ \text{Number of guests choosing beef} = \frac{1}{5}N. \]

2. **Chicken:**  
   \( \frac{11}{20} \) of the guests chose chicken, so:
   \[ \text{Number of guests choosing chicken} = \frac{11}{20}N. \]

3. **Vegetarian:**  
   We know that 145 guests chose vegetarian meals.

4. **Equation Setup:**
   The total number of guests must be the sum of those choosing beef, chicken, and vegetarian meals. So:
   \[
   \frac{1}{5}N + \frac{11}{20}N + 145 = N.
   \]

5. **Combine Like Terms:**
   First, express both fractions with a common denominator.  
   \( \frac{1}{5} = \frac{4}{20} \), so:
   \[
   \frac{4}{20}N + \frac{11}{20}N = \frac{15}{20}N = \frac{3}{4}N.
   \]
   Now the equation becomes:
   \[
   \frac{3}{4}N + 145 = N.
   \]

6. **Solve for \( N \):**
   Subtract \( \frac{3}{4}N \) from both sides:
   \[
   145 = N - \frac{3}{4}N = \frac{1}{4}N.
   \]
   Multiply both sides by 4:
   \[
   N = 145 \times 4 = 580.
   \]

### Final Answer:
There were **580 guests** at the wedding.

---

Would you like a breakdown of any step, or have further questions?

Here are five related questions:
1. What would the answer be if 160 guests chose vegetarian?
2. How would the equation change if 2/5 of the guests chose chicken instead?
3. What percentage of the guests chose vegetarian meals?
4. How many guests chose beef in this problem?
5. Can we express the chicken portion as a percentage instead of a fraction?

**Tip:** Converting all fractions to the same denominator early can simplify equations with multiple fractions.

Meg organized a large wedding. Guests had to choose their meal from beef, chicken, or vegetarian. 1/5 of the guests chose beef, 11/20 of the guests chose chicken, and 145 of the guests chose vegetarian. How many guests were at the wedding?

Learn how to find the total number of guests at a wedding where meal choices are distributed between beef, chicken, and vegetarian options. This problem involves fractions, algebraic equations, and basic arithmetic, making it suitable for middle school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation