Question

At a conference 94 sales managers are discussing ways to expand their respective customer bases. The discussion has been divided into 20 subtopics, with each subtopic discussed by a group of either 4 or 6 people. How many topics will be discussed by all of the 6 person groups together?

Answer 1

7 topics will be discussed by the 6 person groups.

Explanation:

Let F represents the number of topics discussed by 4 persons group and S represents the number of topics discussed by 6 persons group.

There are total 94 persons

4F + 6S = 94

4F = 94 - 6S

F = (94 - 6S)/4 eq. 1

The discussion has been divided into 20 subtopics

F + S = 20 eq. 2

Substitute eq. 1 into eq. 2

(94 - 6S)/4 + S = 20

(94 - 6S)/4 = 20 - S

94 - 6S = 4(20 - S)

94 - 6S = 80 - 4S

- 6S + 4S = 80 - 94

-2S = - 14

S = 14/2

S = 7

Therefore, 7 topics will be discussed by the 6 person groups.

Bonus:

The number of topics discussed by the 4 person groups can be found by substituting the value of S into eq. 1

F = (94 - 6S)/4

F = (94 - 6*7)/4

F = (94 - 42)/4

F = 52/4

F = 13

Verification:

The sum of F and S should be equal to 20 as per eq. 2

F + S = 20

13 + 7 = 20

20 = 20

Hence, solution is verified.