Answer:
Total people = 240
Step-by-step explanation:
Let the total number of people by 'x'.
[tex]\sf \text{Number of men =$ \dfrac{1}{4}*x$} \\[/tex]
[tex]\sf \text{Number of women =$\dfrac{1}{3}x$}[/tex]
Number of children = 100
When we subtract the total number of men and women from the total people 'x', we get the number of children.
[tex]\sf x - \left(\dfrac{1}{4}x+\dfrac{1}{3}x\right)= 100\\\\x - \left(\dfrac{1*3}{4*3}x+\dfrac{1*4}{3*4}x\right)=100\\\\[/tex]
[tex]x- \dfrac{4+3}{12}x=100\\\\x - \dfrac{7}{12}x = 100\\\\ \dfrac{12}{12}x-\dfrac{7}{12}x = 100\\\\ \dfrac{5}{12}x=100\\[/tex]
[tex]\sf x = 100*\dfrac{12}{5}\\[/tex]
x = 20 * 12
x = 240
Total number of people = 240
