**At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.a) Find the ratio of male speakers to male participants at the conference.b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?Solution**

Male ----- 120%

Female ----- 100%

Speakers

Male : Female

8 (parts) : 5 (parts)

Participants

Male : Female

1 (unit) : 1 (unit)

Men ----- 8 parts + 1 unit

Women ----- 5 parts + 1 unit

But since there are 20% more women than men,

Women ----- 5 parts x 120% + 1 unit x 120%

= 6 parts + 1.2 units

Men ----- Women

8 parts + 1 unit ----- 6 parts + 1.2 units

8 parts - 6 parts ----- 1.2 units - 1 unit

2 parts ----- 0.2 unit

1 part ----- 0.1 unit

10 parts ----- 1 unit

or

1 unit ----- 10 parts

**(a)**

Male Speakers ----- 8 parts

Male Participants ----- 1 unit or 10 parts

Male Speakers : Male Participants

8 : 10

4 : 5

**Answer: 4 : 5**

**(b)**

Speakers

Male : Female

8 (parts) : 5 (parts) -- (altogether 13 parts)

Participants

Male : Female

1 (unit) : 1 (unit)

10 (parts) : 10 (parts) -- (before)

- 40 : + 60 -- (40 males left; 60 females joined)

3 (units) : 4 (units) -- (3/4 as many male as females in the end)

(Male) 3 units ----- 10 parts - 40

(Female) 4 units ----- 10 parts + 60

(Female) - (Male)

4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)

1 unit ----- 60 + 40

1 unit ----- 100

(Male after)

3 units ---- 3 x 100 = 300

(Male before)

10 parts ---- 300 + 40 (need to add the 40 who left)

10 parts ----- 340

1 part ---- 34

All speakers

13 parts ---- 13 x 34 = 442

Answer: 442 speakers

Answer: 442 speakers

Printer Friendly Version

## No comments:

Post a Comment