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.

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