Answer:
There are 198 children at the circus show.
Step-by-step explanation:
Let the total number of spectators be 'x'.
Given:
Number of men = [tex]\frac{1}{4}[/tex] of the total number
Number of women = [tex]\frac{2}{5}[/tex] of the remaining number.
Also, number of women = 132
Number of men = [tex]\frac{1}{4}\ of\ x=\frac{x}{4}[/tex]
Now, spectators remaining = Total number - Number of men
Spectators remaining = [tex]x-\frac{x}{4}=\frac{4x-x}{4}=\frac{3x}{4}[/tex]
Now, number of women = [tex]\frac{2}{5}\times \frac{3x}{4}=\frac{6x}{20}[/tex]
Now, as per question:
Number of women = 132. Therefore,
[tex]\frac{6x}{20}=132[/tex]
[tex]6x=132\times 20[/tex]
[tex]x=\frac{2640}{6}=440[/tex]
Therefore, the total number of spectators = 440
Also, number of men = [tex]\frac{x}{4}=\frac{440}{4}=110[/tex]
Now, total number of spectators is the sum of the number of men, women and children.
Let the number of children be 'c'.
Total number = Men + Women + Children
[tex]440=110+132+c\\440=242+c\\c=440-242=198[/tex]
Therefore, there are 198 children at the circus show.
