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
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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) (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) (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) (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
= number of men
Therefore the other = number of women and children
= number of women
= number of women
Number of children = Number of Women + 400
Number of children =
Women and Children=
Women and Children=
Women and Children=
Women and Children=
Multiply both sides by
Check:
Men =
Women =
Children = Women + 400 =
Total = 1800 so it checks!!
R^2 at SCC
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