Question

A room contains 96 people. A man leaves and is replaced by a woman, leaving three times as many women as men in the room. How many men and how many women were there originally?

Answer 1

Let's use 'M' and 'W' to represent the number of men and women in the room originally. Can you write an equation that states the total number of people was 96?

Answer 2

i guess some thing like this, 96-M=96+W. but im not sure

Answer 3

You're over-thinking it :-) ... it's just M + W = 96.

Answer 4

So whats going to be the other equation?

Answer 5

OK, let's call that equation 1 and leave it for a second. Now we need equation 2. First, how many men are there in the room (in terms of M) after one man leaves? And, how many women after a woman arrives?

Answer 6

After one man leaves and women arrives

Answer 7

right.

Answer 8

so that brings to this 96-M=96+W right?

Answer 9

no. I'm thinking of something simpler. If there are M men in the room, and one leaves, now how many are there?

Answer 10

M-1?

Answer 11

Right. And after one woman arrives how many are there?

Answer 12

W+1?

Answer 13

Right. You're on your way. Now, let's say hypothetically, the question said that that after a man leaves, and a woman arrives, there are the same number of men and women in the room. How could you write that as an equation?

Answer 14

M-1=W+1 ?

Answer 15

yes, exactly! One more step. What the problem actually says is that, after the replacement, there are 3 times as many women in the room. Another way of saying this is that the number of women is equal to 3 times the number of men. Can you now translate that into an equation?

Answer 16

\( 3\times (M-1) =( W+1) \)

Answer 17

So is that the second equation?

Answer 18

I think so.

Answer 19

yep.

Answer 20

Now solve it tot get M, and W ...

Answer 21

Now you have 2 equations with 2 unknowns, so solve simultaneously. The substitution method is probably easiest here.

Answer 22

Ok