# Percentage problem

1. Jun 17, 2014

### galois

99% of the people in a room are men. How many men would have to leave the room in order for this percentage to decrease to 98%? It is known that the number of women in the room is 3.

I get stuck on this one.I'm not sure if my result is good i got 2.97 !

2. Jun 17, 2014

### 1MileCrash

No, your solution is not close.

How many people are there total? Answer me that first.

3. Jun 17, 2014

### SteamKing

Staff Emeritus
It's chopping off that 0.03 of the third guy which could be a problem.

Percentage problems are like proportion problems, they just use a different way to express the proportion, with a percentage instead of a ratio.

You know the number of women in the room, but you don't know the number of men. Call the number of men 'x' and write an equation which expresses the original percentage of men to the total number of men and women. You should be able to solve this equation for the number of men. Write another equation, using the second percentage and solve it. The difference in the values of 'x' from the two equations will be the number of men asked to leave.

4. Jun 18, 2014

### galois

There are 3 women in the room,so they make 1% of people in the room.That means there are 300 in total.

5. Jun 18, 2014

So that means there are 297 males in the room.
We know that 1% = 3, and 99-98 =1 So how many man will have to leave the room?

No need of doing many calculation here.

6. Jun 18, 2014

### galois

3 1
--- = --- , 300 = x
x 100

297 of them men. For the same 3 women to make up 2% of a room, there
have to be 150 people in the room,

3 2
--- = --- , 300 = 2x , 150 = x
x 100

147 of them men. 150 men have to leave the room I think.

7. Jun 18, 2014

### galois

99:x=100:300
29700=100x
x=297

98:x=100:300
29400=100x
x=294

297-294=3

294 is 98% of 297. Is this right ?

8. Jun 18, 2014

Yes, the answer is 3.
No 294 is 98% of 300.

9. Jun 18, 2014

### galois

My bad,can you please write the proportions for me,i understand what SteamKing means.

10. Jun 18, 2014

This is how you do it.

11. Jun 18, 2014

### galois

I'm confused now.Can you please write the solution. sorry if i'm troubling you.

12. Jun 18, 2014

### galois

Please I need the result really.If i knew how to solve it I wouldn't ask you,so please write how to solve this.I do not want to be rude. Help please :D

13. Jun 18, 2014

Let's see now. We have 300 people. 297 is male(99% of 300) and 3 is female.

Now $\frac{98}{100} \times 300= 294$- This means that 98% of the people is 294.
The difference between 297-294 is 3

So when 3 males get out, the percentage of males will change from 99% to 98%.

The total number of people will decrease from 300 to 297

Now, what is the other 2 percent? This made me confused too. From where did you get this question?

14. Jun 18, 2014

### galois

Yes i get to this point to,but can't finish it i have some ideas,but I'm not sure if they are right.I got this problem from my professor to solve.

Do you think this could be the solution

3 1
--- = --- , 300 = x
x 100

297 of them men. For the same 3 women to make up 2% of a room, there
have to be 150 people in the room,

3 2
--- = --- , 300 = 2x , 150 = x
x 100

147 of them men. 150 men have to leave the room I think.

Last edited: Jun 18, 2014
15. Jun 18, 2014

### 1MileCrash

Yes, the answer is 150, you have worked the problem exactly correct.

Adjacent seems to be confused here. 3 males getting out does not change the percentage to 98% because you don't have 300 people any more. 98% of 300 and 98% of some changed total are different animals.

I did it differently, but it amounts to the same thing, and I think your solution is much more clever, because while I looked at the men (which is a changing value) you looked at the women, which would not change, to solve the same problem. This was a very good thing you did.

297 / 300 = .99,

We would like to subtract an "x" from the numerator and denominator because men leaving decreases the number of men, 297, and the number of people, 300.

So I solved the equation:
(297-x)/(300-x) = .98
Which quickly yields x = 150.

This is how I instinctively solved it, but again, I like what you did better.

Last edited: Jun 18, 2014
16. Jun 18, 2014

I don't think so. I didn't understand his workings.
If 150 people left the room then there should be 147 men in the room left.
--> $\frac{147}{297} \times 100=49.494949...$
--> That means the percentage of men in the room is 49.494949...%
Then the percentage of women is calculated like this:$\frac{3}{297} \times 100=1.1010101...%$
So the total percentage is 50.5050505...%?

17. Jun 18, 2014

### 1MileCrash

No, it is clear. Galois reasoned that the static number of women, 3, will be 2% of the new total. Thus, the new total is 150. Therefore the total decreased by (300 - 150) = 150. Done.

If 150 men leave the room, there are (297-150) = 147 men in the room. If 150 men leave the room then there are (300-150) = 150 people left in the room total. 147 is 98% of 150. What is your objection? The expressions you wrote aren't about anything in this problem.

Last edited: Jun 18, 2014
18. Jun 18, 2014