Agroup of 266 persons consists of men, woman, and children. there are four times as many mens as children and twice as many as woman as children. how many of each are there.

There are 38 children, 152 men, and 76 women in the group.

Solution:

Given that group of 266 persons consists of men, woman, and children

Let "c" be the number of children

Given that There are four times as many mens as children

Number of mens = 4(number of children)

number of men = 4c  --- eqn 1

And twice as many as woman as children

Number of woman = 2(number of children)

number of woman = 2c eqn 2

Given there are a group of 266 persons consists of men, woman, and children

number of men + number of woman + number of children = 266

Substitute eqn 1 and eqn 2 in above expression

4c + 2c + c = 266

7c = 266

c = 38

Thus from eqn 1,

number of men = 4c = 4(38) = 152

From eqn 2,

number of woman = 2c = 2(38) = 76

Thus there are 38 children, 152 men, and 76 women in the group.