Question

At a soccer match , 60% of the spectators are men and the rest are women and children .The number of children is 2/3 of the women.There are 252 more men than women at the soccer match.How many spectators are there altogether.

Answer 1

Answer:

Step-by-step explanation:

We need a series of equations to be able to sub back and forth into one another in order to get this down to one variable, s for spectators.  This is what we know from the info (in algebraic expression/equation form):

.6s = men (60% of the spectators are men)

.4s = women + children (40% of the spectators are women and children)

# of children = 2/3 women

# of men = women + 252 (There are 252 more men than women) and

# women = men - 252

Those are the equations we need to solve for the number of spectators.

Start at the top with

.6s = men.  We know that the number of men = women + 252, so

.6s = women + 252.

.4s = women + children. We know that the number of children is 2/3 the number of women, so

.4s = women + 2/3 women.  If the number of men = women + 252, then

.4s = men - 252 + 2/3(men - 252) which simplifies to

.4s = 3/3 men - 252 + 2/3 men - 168 and

.4s = 5/3 men - 420 and

.4s = s - 420 and

-.6s = -420 so

s = 700

Answer 2

There are 700 spectators altogether.

Let the total number of people = x

60% of the spectators are men. So, 0.60x are men.

Rest are women and children . So (x - 0.60x) = 0.40x are women and children.

The number of children is 2/3 of the women.

Let there are w women.

So there are 2w/3 children.

So,

$w+\frac{2w}{3}=0.40x\\\frac{5w}{3}=0.40x\\w=0.40x\cdot\frac{3}{5}\\w=0.24x$

Given that: there are 252 more men than women at the soccer match.

So,

$0.60x-0.24x=252\\0.36x=252\\x=700$

There are 700 spectators altogether.

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