Answer:
[tex]Adults = 510[/tex]
Step-by-step explanation:
Given
[tex]Children = \frac{3}{5}[/tex]
[tex]Girls:Boys = 2 : 7[/tex]
[tex]Girls = 170[/tex]
Required
Determine the number of adults
First, we need to calculate the number of children
[tex]Girls:Boys = 2 : 7[/tex]
Given that: [tex]Girls = 170[/tex]
Substitute 170 for Girls in [tex]Girls:Boys = 2 : 7[/tex]
[tex]170 : Boys = 2 : 7[/tex]
Convert to fraction
[tex]\frac{170}{Boys} = \frac{2}{7}[/tex]
Cross Multiply
[tex]Boys * 2 = 170 * 7[/tex]
Divide both sides by 2
[tex]Boys = \frac{170 * 7}{2}[/tex]
[tex]Boys = \frac{1190}{2}[/tex]
[tex]Boys = 595[/tex]
So, the number of children are:
[tex]Children = Boys + Girls[/tex]
[tex]Children = 595 + 170[/tex]
[tex]Children = 765[/tex]
Next, we calculate the number of people in the cinema.
[tex]Children = \frac{3}{5} * People[/tex]
Substitute 765 for Children
[tex]765 = \frac{3}{5} * People[/tex]
Make People the subject.
[tex]People = \frac{765 * 5}{3}[/tex]
[tex]People = \frac{3825}{3}[/tex]
[tex]People = 1275[/tex]
If 3/5 are children, then 2/5 are adults.
So:
[tex]Adults = \frac{2}{5} * 1275[/tex]
[tex]Adults = \frac{2* 1275}{5}[/tex]
[tex]Adults = \frac{2550}{5}[/tex]
[tex]Adults = 510[/tex]
