2500 people took part in a race. The number of adults was 4 times the number of children. There were 1200 men. How many women were there?

The total number of women (w) = 800

Step-by-step explanation:

We can express the total number of each group as follows;

Total number of people (p) = Number of Adults (a) + number of children (c)

2,500=a+c ... equation 1

Number of Adults (a) = 4*number of children (c)

a=4 c ... equation 2

Replacing the value of a in equation 1 with the value for a in equation 2

2,500=4 c+c

5 c=2,500

c=2,500/5

c=500

Number of children (c) = 500

Replace the value of c in equation 2 with 500 and solve

a=4*500

a=2,000

Number of adults (a) = 2,000

But the total number of adults can be expressed as;

Total number of adults (a) = Total number of men (m) + total number of women (w)

a=m+w

where;

a=2,000

m=1,200

replacing;

2,000=1,200+w

w=2,000-1,200

w=800

The total number of women (w) = 800