Question

In a survey of employees at a fast food restaurant, it was determined that 13 cooked food, 14 washed dishes, 23 operated the cash register, 5 cooked food and washed dishes, 8 cooked food and operated the cash register, 10 washed dishes and operated the cash register, 4 did all three jobs, and 7 did none of these jobs. How many employees were surveyed?

a) 42
b) 53
c) 65
d) 79

Answer 1

To find out how many employees were surveyed, we can use the principle of inclusion-exclusion.

Step-by-step explanation:

To find out how many employees were surveyed, we can use the principle of inclusion-exclusion. Let's start by adding up the number of employees who performed each individual job:

Cooked food: 13

Washed dishes: 14

Operated the cash register: 23

Next, we subtract the number of employees who performed two jobs:

Cooked food and washed dishes: 5

Cooked food and operated the cash register: 8

Washed dishes and operated the cash register: 10

Now, we need to add back the number of employees who performed all three jobs:

Cooked food, washed dishes, and operated the cash register: 4

Finally, we subtract the number of employees who did none of these jobs:

None of these jobs: 7

By adding up the individual jobs, subtracting the number of employees who performed two jobs, adding back the number of employees who performed all three jobs, and subtracting the number of employees who did none of these jobs, we can find out how many employees were surveyed. In this case, 53 employees were surveyed. Therefore, the answer is option (b) 53.