Question

A group of 266 persons consist of men, women, and children. There are four times as many men as children. And twice as many women as children. How many of each are there

Answer 1

There are 152 men, 76 women and 38 children.

Step-by-step explanation:

Total persons = 266

Let,

men = m

women = w

children = c

According to given statement;

m+w+c=266    Eqn 1

m = 4c   Eqn 2

w = 2c   Eqn 3

Putting value of m and w from Eqn 2 and 3 in Eqn 1

$4c+2c+c=266\\7c=266$

Dividing both sides by 7

$\frac{7c}{7}=\frac{266}{7}\\c=38$

Putting c=38 in Eqn 2;

$m=4(38)\\m=152$

Putting c=38 in Eqn 1;

$w=2(38)\\w=76$

There are 152 men, 76 women and 38 children.

Keywords: linear equations, substitution method

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