Question

A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 people attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only?(1) 3/4 of the people attended both sessions(2) 7/8 of the people attended the afternoon session

Answer 1

16 people attended the morning session only

Explanation:

Total number of people attending the seminar = 128

Let M represent those dat attended the morning session.

Let A represent those that attended the afternoon session.

We are told that 3/4 of the people attended both sessions.

3/4*128 = 96

96 people attended both sessions

We are also told that 7/8 people attended afternoon session.

7/8*128 = 112

112 people attended the afternoon session.

To find those that attended the morning session only, we will use a Venn diagram

x -96 + 96 + 16 = 128

x = 128 -16

x = 112

Those that attended the morning session only = x - 96

= 112 - 96

= 16

16 people attended the morning session only

Answer 2

16 people

Explanation:

This is a set problem

let first session be a

let second session be b

128 people attended at least one session = a∪b

a. 3/4 attended both session 1&2 = a∩b

b. 7/8 attended session 2 = p(b) i.e population b

c x attended session 1 = p(a) i.e. population a

lets get the figures.

• For both sessions 3/4 × 128 = 96 = a∩b
• For second session 7/8 × 128 = 112 = b
• The formular is a∪b = p(a) + p(b) - a∩b
• a∪b = 128 (they at least one session)

lets substitute into the equation

let p(a) be x

128 = x + 112 - 96

128 = x + 16

x = 112 - no of people that attended the morning session.

But to find those that ONLY attended morning session

x - a∩b

112 - 96 = 16