How many people are there in room A after the change of rooms (below)?
There were 1200 people in Room A and Room B. 30% of 800 people in Room A were women. 40% of the people in Room B were men. After some people in both rooms had changed rooms, 25% of the people in Room A and 75% in room B were women.
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Number of people in Room A initially = 800
Number of people in room B initially = 1200-800 = 400
In room A initially there were 30% of 800 are women.
Number of women in room A initially = 30/100*800 = 240
Number of men in room A initially = 800-240 = 560
In room B initially there were 40% 400 are of men.
Number of men in room B initially = 40/100*400 = 160
Number of women in room B initially = 400-160 = 240
Total number of men = 160+560 = 720
Total number of women = 240+240 = 480
Number of people in room A = x
Number of people in room B = 1200-x
So after change 25% of people in room A and 75% in room B are women. But total women ill be 480.
0.25x+0.75(1200-x) = 480
x = 840
So there are 840 people in room A after change.
Let, A - # of people in Room A
B - # of people in Room B
The total number of people in A and B is 1200. So we have,
> Then, let's consider the number of people in Room A.
`A_f + A_m = A`
where `A_f` and `A_m` represents the number of females and males in Room A.
The given values for Room A are:
`A=800 ` `A_f = 0.30(800)=240`
Then, let's solve for `A_m` .
> Next, let's consider the number of people in Room B.
Susbtituting value of A to EQ.1, then Room B has:
The given number of males in Room B is:
Then, solve for number of females in Room B. `B_f` is:
`B_f + B_m=400`
So we have,
Room A Room B Total
#of females: 240 240 480 (total # of females)
# of males : 560 160 720 (total # of males)
Total # of People: 800 400 1200
> When some of the people changed rooms, we have
Note that the total number of females in both room is still the same which is 480. So,
`A'_f + B'_f=480`
To solve for A' (new # of people in Room A), express EQ.2 in one variable. To do so, we need to take note that the total number of people is both rooms is unchanged.
Subtitute this to EQ.2 .
Hence, after some of the people changed rooms, Room A has a total of 840 people.
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