3 set problem

Question

a supermarket compiled the following information regarding 30 of its employees. 8 worked in the produce department, 9 stacked food on shelves, 18 operated the cash register, 4 worked in the produce department and stacked food at different times, 5 worked in the produce department and operated the cash register at different times, 3 stacked food and operated the cash register at different times, 2 did all three jobs at different times. how many of the employees i) did at least two of the jobs, ii) worked in produce only, iii) did only one of the jobs, iv) stacked shelves or operated the cash register, v) stacked shelves and operated the cash register but did not work in produce

Answer 1

Problems of this type are easily solved using Venn Diagrams.  Usually, the solution takes the information in reverse order to find specific numbers and solve the problem.

                 

Since I can't draw a nice diagram, imagine three intersecting circles inside a large box:

 

         H (none)

 

                Circle Produce                     Circle Stack

 

                          G                                     F

                                              D

 

                                              A

 

                                 C                      B

                                                

 

                                               E

 

                                           Circle Register

 

1. "30 of its employees"    means   A+B+C+D+E+F+G+H = 30

2. "8 worked in the produce department" means    A+C+D+G = 8

3. "9 stacked food on shelves"  means    A+B+D+F = 9

4. "18 operated the cash register"   means  A+B+C+E = 18

5. "4 worked in the produce department and stacked food "  means   A+D = 4

6. "5 worked in the produce department and operated the cash register"  means  A+C = 5

7.  "3 stacked food and operated the cash register"   means  A+B = 3

8.  "2 did all three jobs"   means  A = 2

 

Use 8:              A=2

Using 8 with 7: B=1

Now, solve 6:   C=2

Now, solve 5:   D=4

Now, solve 4:   E=13

Now, solve 3:   F=2

Now, solve 2:   G=1

Now, solve 1:   H=5

TOTAL:               30

 

This makes the questions easy:

  i)  A+B+C+D = _____

 ii)  G = ____

iii)  E+F+G = ______

iv)  A+B+C+D+E+F = ______

v)  B = ____