Maths Question Need Help

[Tohto]

There were 280 people at a concert. 25% of the men and 20% of the women wore glasses.

Given that a total of 60 people wore glasses in the concert, how many men wore glasses?

Edited March 25, 2012 by Tohto

[Whitepowder]

20.

 

total nos of men = X

total nos of women = 280 - X

Nos of Men and Women with glasses =0.25 * X+ (280 - X) * 0.2 = 60 =====> X = 80

 

Nos of Men and Women with glasses = 0.25 * X ======> 20

[1fast1]

There were 280 people at a concert. 25% of the men and 20% of the women wore glasses.

Given that a total of 60 people wore glasses in the concert, how many men wore glasses?

 

Can't use algebra, I assume. Let's use a simple model.

 

Denote 1 man unit by a square, and 1 woman unit by a circle.

 

Let all the people at the concert be denoted by 4 squares and 5 circles. This doesn't matter since the size of a unit is arbitrary. The choice of those numbers is guided by the need to evenly divide the men by 4 (25%) and the women by 5 (20%).

 

25% of the men = 1 square. 20% of the women = 1 circle.

 

So 1 square + 1 circle = 60. Hence 4 squares + 4 circles = 4*60 = 240.

 

But we know that 4 squares + 5 circles = 280. Hence 1 circle = 40. All the women (5 circles) = 200, so all the men = 280-200 = 80, and 25% of the men = 80/4 = 20.

 

The reason I used different notations (square and circle) to denote men and women rather than a single bar is because we don't know the relative proportion of men to women a priori.

Edited March 25, 2012 by Turboflat4

[1fast1]

Can't use algebra, I assume. Let's use a simple model.

 

Denote 1 man unit by a square, and 1 woman unit by a circle.

 

Let all the people at the concert be denoted by 4 squares and 5 circles. This doesn't matter since the size of a unit is arbitrary. The choice of those numbers is guided by the need to evenly divide the men by 4 (25%) and the women by 5 (20%).

 

25% of the men = 1 square. 20% of the women = 1 circle.

 

So 1 square + 1 circle = 60. Hence 4 squares + 4 circles = 4*60 = 240.

 

But we know that 4 squares + 5 circles = 280. Hence 1 circle = 40. All the women (5 circles) = 200, so all the men = 280-200 = 80, and 25% of the men = 80/4 = 20.

 

The reason I used different notations (square and circle) to denote men and women rather than a single bar is because we don't know the relative proportion of men to women a priori.

 

Even faster,

 

5 squares + 5 circles = 300. So 1 square = 300 - 280 = 20, and that's the answer, since 1 square represents the number of men wearing glasses.

[WTF]

Even faster,

 

5 squares + 5 circles = 300. So 1 square = 300 - 280 = 20, and that's the answer, since 1 square represents the number of men wearing glasses.

Wah lao bro, your first solution I can still understand. Your second one confused me liao.......

 

Perhaps I'm too stupid.....

[1fast1]

Wah lao bro, your first solution I can still understand. Your second one confused me liao.......

 

Perhaps I'm too stupid.....

 

Hi bro, same principle, just multiply by 5 instead of 4.

 

1 square + 1 circle = 60

 

5 squares + 5 circles = 5*60 = 300

 

Since 4 squares + 5 circles (all the people) = 280,

 

1 square = 300 - 280 = 20.

 

Since 1 square represents the men who wore glasses, this is the answer.

[WTF]

Hi bro, same principle, just multiply by 5 instead of 4.

 

1 square + 1 circle = 60

 

5 squares + 5 circles = 5*60 = 300

 

Since 4 squares + 5 circles (all the people) = 280,

 

1 square = 300 - 280 = 20.

 

Since 1 square represents the men who wore glasses, this is the answer.

Thank you beri much, bro!!!