A professor gave a speech to an assembly of colleagues. After five minutes, half of the audience left; 10 minutes later a third of the remaining audience left. After 20 more minutes, half of the remaining audience left, leaving only 3 people in the audience. How many people were in the audience at the beginning of the speech?
2007-09-17 02:39:18 · 13 answers · asked by Barbie 1 in Science & Mathematics ➔ Mathematics
Let audience number = x at start.
After 5 mins audience = x/2
10 minutes later audience = x/2 - x/6 = x/3
20 minutes later audience = x/3 - x/6 = x/6
x/6 = 3
x = 18
18 people present at start.
2007-09-18 04:35:12 · answer #1 · answered by Como 7 · 1⤊ 0⤋
Do this in reverse, using reciprocals.
3 x 2 = 6 : this many left before half left. Reciprocal of 1/2 is 2
6 x 3/2 = 9 : remember 1/3 left so 2/3 remain. Use reciprocal of 2/3, which is 3/2
9 x 2 = 18 : people there before any left. Reciprocal of 1/2 used here again
So he started giving his speech to 18 people.
Check : 18 x 1/2 = 9 : after 5 minutes
9 x 2/3 = 6 :10 minutes later
6 x 1/2 = 3 : 20 more minutes
3 people in the audience
2007-09-17 09:57:58 · answer #2 · answered by Don E Knows 6 · 0⤊ 1⤋
Let x = No. of people.
No.of X Time.
x t = 0
x/2 t = 5
x/2 - x/2÷3 t=15
x/2 - x/2*1/3
x/2 - x/6
(3x - x)/6
x/3
x/3 ÷ 2 t=35
x/3*½
x/6
x/6 = 3
x = 3*6
x = 18
Check : 18 x 1/2 = 9 : after 5 minutes
9 x 2/3 = 6 :15 minutes later
6 x 1/2 = 3 : 35 more minutes
3 people in the audience
2007-09-17 10:02:37 · answer #3 · answered by Sparks 6 · 0⤊ 1⤋
x = total number of people in the audience
1/2 x = number of people who left after 5 minutes
1/3 (1/2x) = number of people who left after 10 minutes
or 1/6x
after this, the remaining audience should be:
x - (1/2x + 1/6x) = x - (3/6x + 1/6x) = x - 4/6x = 2/6x
Therefore, 1/2 of the remaining audience who left after 20 minutes will be:
1/2 (2/6x) = 2/12x or 1/6x
Equation:
x - (1/2x + 1/6x + 1/6x) = 3
LCD is 6
x - (3/6x + 1/6x + 1/6x) = 3
x - 5/6x = 3
1/6x = 3
Multiply both equations by 6
x = 18
To check:
1/2 of the audience left after 5 minutes (1/2 of 18) = 9
1/3 of 9 people left after 10 minutes = 3
After 12 people left, only 6 remained (18 - 9 - 3)
1/2 of 6 = 3 (number of people left after 20 minutes)
18 - (9 + 3 + 3) = 3
2007-09-17 09:58:48 · answer #4 · answered by edith p 3 · 0⤊ 1⤋
Go backwards to figure it out:
Final number of people left: 3 people
20 more minutes, half so 3 * 2: 6 people
10 minutes one third was added so (1/3)*6 + 6 : 9 people
five minutes half, 2* 9: 18 people
Final answer 18 people at the beginning
-----------------------------------------------
Now verify the answer
Start with 18
5 min, half. 18/2 = 9
10 min 1/3 left: 9 - (9 / 3) = 6
20 mins 1/2: 6/2 = 3 left
2007-09-17 10:01:37 · answer #5 · answered by petep73 3 · 0⤊ 1⤋
18
2007-09-17 09:49:44 · answer #6 · answered by rmtzlr 2 · 0⤊ 1⤋
let x = audience at the beginning of the speech
after 5 min. - x/2 audience left; remained: x/2
10 min later- (x/2)/3 audience left; remained:x/2 - (x/2)/3] = x/3
after 20 min more - (x/3)/2 audience left; remained: x/3 - (x/3)/2 = x/6 = 3 .... x=18
let's check..
initial # of audience: 18
--------------------- left --------------- remained
after 5 min ------ 9 --------------- 9
after 10 min ----- 3 --------------- 6
after 20 min ----- 3 --------------- 3
2007-09-17 10:08:02 · answer #7 · answered by Enginurse 2 · 0⤊ 1⤋
3=1/2 of 6
6=2/3 of 9
9= 1/2 of 18
there were 18 people at the beginning
2/3(x/2)/2=3
x=18
2007-09-17 09:54:00 · answer #8 · answered by bignose68 4 · 0⤊ 1⤋
number of people = x
after 5 minutes = x/2
after 10 minutes = 1/3(x/2)=x/6
after 20 minutes =1/2(x/6) = x/12
x/12=3
x=36 people.
2007-09-17 10:00:44 · answer #9 · answered by cidyah 7 · 0⤊ 2⤋
At the beginning there were 100% of people. LOL
Maybe,16 but really, your question in missing more information
2007-09-17 09:49:16 · answer #10 · answered by Anonymous · 0⤊ 1⤋