In a survey of employees at a fast food​ restaurant, it was determined that 14 cooked​ food, 16 washed​ dishes, 25 operated the cash​ register, 6 cooked food and washed​ dishes, 7 cooked food and operated the cash​ register, 9 washed dishes and operated the cash​ register, 4 did all three​ jobs, and 5 did none of these jobs. How many of the employees washed dishes and operated the cash register but did not cook​ food?

To determine the number of employees who washed dishes and operated the cash register but did not cook food, we can break down the problem using set notation.

### Given:
- \( |C| = 14 \) (employees who cooked food)
- \( |D| = 16 \) (employees who washed dishes)
- \( |R| = 25 \) (employees who operated the cash register)
- \( |C \cap D| = 6 \) (employees who cooked food and washed dishes)
- \( |C \cap R| = 7 \) (employees who cooked food and operated the cash register)
- \( |D \cap R| = 9 \) (employees who washed dishes and operated the cash register)
- \( |C \cap D \cap R| = 4 \) (employees who did all three jobs)
- \( |None| = 5 \) (employees who did none of these jobs)

### Step 1: Identify the relevant set
We are interested in finding the number of employees who:
- Washed dishes \((D)\)
- Operated the cash register \((R)\)
- Did **not** cook food \((\text{not } C)\)

### Step 2: Calculate the required number
The number of employees who washed dishes and operated the cash register but did not cook food can be calculated by subtracting those who did all three jobs from those who did both \(D\) and \(R\):
\[
|D \cap R \cap \text{not } C| = |D \cap R| - |C \cap D \cap R|
\]
Substituting the values:
\[
|D \cap R \cap \text{not } C| = 9 - 4 = 5
\]

### Final Answer:
The number of employees who washed dishes and operated the cash register but did not cook food is **5**.

Would you like more details or have any questions about this?

Here are some related questions you might find interesting:
1. How many employees did exactly two jobs?
2. How many employees washed dishes but did not operate the cash register or cook food?
3. How many employees did only one job?
4. How many employees did at least one of the three jobs?
5. How many employees cooked food and washed dishes but did not operate the cash register?

**Tip:** When dealing with set operations like this, drawing a Venn diagram can help you visualize the intersections and differences between sets.

Learn how to calculate the number of employees who washed dishes and operated the cash register but did not cook food using set theory. This problem involves finding intersections and differences between sets in a survey of employees at a fast food restaurant.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation