math homework...

Question

In a survey of employees at a fast food​ restaurant, it was determined that 15 cooked​ food, 13 washed​ dishes, 18 operated the cash​ register, 6 cooked food and washed​ dishes, 5 cooked food and operated the cash​ register, 6 washed dishes and operated the cash​ register, 2 did all three​ jobs, and 7 did none of these jobs. how many employees were there surveyed in total?

Answer 1

I think this can be solved by drawing a Venn diagram with 3 overlapping circles for 3 overlapping sets.

Set A: 15 employees that cooked​ food

Set B: 13 employees that washed​ dishes

Set C: 18 employees that operated the cash​ register

and one isolated circle for the last set

Set D: 7 employees that did none of these jobs

The total number of employees that were there surveyed is determined by adding up the 8 components of the Venn diagram describing sets A, B, C, and D.

2 employees did all 3 jobs (A∩B∩C)

4 more employees cooked food and washed​ dishes (A∩B)

4 more employees washed dishes and operated the cash​ register (B∩C)

3 more employees cooked food and operated the cash​ register (A∩C)

6 more employees only cooked food (the non-intersecting part of A)

3 more employees only washed dishes (the non-intersecting part of B)

9 more employees only operated the cash​ register (the non-intersecting part of C)

7 employees did none of these jobs (D)

————————————————————————————————————

2+4+4+3+6+3+9+7=38 total

Answer

38 employees were there surveyed in total

Answer 2

Begin this problem with a large square. Draw 3 overlapping circles inside it. Label one circle Dishes, another circle Cook and the third circle Register.

Now read the problem BACKWARDS.

7 did none of these jobs so put a 7 inside the square but NOT in any circle.

2 did all three jobs so put a 2 in the section where all three circles overlap

6 washed dishes and operated the cash register. So locate that section in the diagram. There is already a 2 in that section so the other part will need a 4.

5 cooked food and operated the cash register. So locate that section in the diagram. There is already a 2 in that section so the other part will need a 3.

6 cooked food and washed dishes. So locate that section in the diagram. There is already a 2 in that section so the other part will need a 4.

18 operated the cash​ register. So locate that section in the diagram. There is already a 4, 2 and 3 in that section so the other part will need a 9.

13 washed​ dishes. So locate that section in the diagram. There is already a 4, 4 and 2 in that section so the other part will need a 3

15 cooked food. So locate that section in the diagram. There is already a 4, 2 and 3 in that section so the other part will need a 6.

All sections are filled so now add the numbers for the total employees surveyed. The answer is 38.