SOLUTION: 1/9 of the people in a stadium are men. 3/8 of the remainder are women and the rest are children. There are 400 more children than women. How many people are there in the stadium a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1/9 of the people in a stadium are men. 3/8 of the remainder are women and the rest are children. There are 400 more children than women. How many people are there in the stadium a      Log On


   

Question 35460: 1/9 of the people in a stadium are men. 3/8 of the remainder are women and the rest are children. There are 400 more children than women. How many people are there in the stadium altogether?
Found 3 solutions by stanbon, mukhopadhyay, rapaljer:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1/9 of the people in a stadium are men. 3/8 of the remainder are women and the rest are children. There are 400 more children than women. How many people are there in the stadium altogether?
Let the number of people in the stadium be "x".
# of men is (1/9)x
# of women is (3/8)[(8/9)x)]= (1/3)x
# of children is (1/3)x+400
EQUATION:
men + women + children= all in the stadium
(1/9) x + (1/3) x + (1/3) x + 400 = x
(7/9) x + 400 = x
(2/9) x = 400
x= 1800 (number of people in the stadium)
Cheers,
Stan H.

Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
Men = 1/9 of the entire population
Remaining = 1 - 1/9 = 8/9;
Women = 3/8 of Remaining = (3/8)(8/9) = 3/9 = 1/3;
Children = Rest of the population = 8/9 - 1/3 = 5/9 of the entire population;
Children population = 400 + Women Population
=> Children population - Women Population = 400;
Children population - Women Population = 5/9 - 1/3 = 2/9 of the population;
So, 2/9 of the population = 400
=> Population = 400*9/2 = 1800
Answer: There are 1800 people in the stadium altogether.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
With a little more thought, someone will probably come up with a cleaner and easier way to do this, but this is what I got for now. It's a neat problem. Nice one!!

Let x = total number of people in the stadium
x%2F9 = number of men

Therefore the other 8x%2F9 = number of women and children

%283%2F8%29%2A%28%288x%29%2F9%29 = number of women
x%2F3+ = number of women

Number of children = Number of Women + 400
Number of children = %28x%2F3%29+%2B+400
Women and Children= %288x%29%2F9+=+%28x%2F3%29++%2B+%28x%2F3%29+%2B+400
Women and Children= %288x%29%2F9+=+%282x%2F3%29++%2B+400
Women and Children= %288x%29%2F9+=+%286x%2F9%29+%2B+400
Women and Children= %282x%29%2F9+=++400

Multiply both sides by 9%2F2
%282x%29%2F9+%2A%289%2F2%29+=++400%2A%289%2F2%29+
x+=+1800+

Check:
Men = 1800%2F9+=+200
Women = +1800%2F3+=+600
Children = Women + 400 = 600%2B400+=+1000
Total = 1800 so it checks!!

R^2 at SCC