Question

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?

Answer 1

Answer:

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