Answer :
Ok, there is an equation you can use to solve it.
n is a number.
p is also a number, but different to n.
[tex]\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } \cdot 1=\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } =\frac { p }{ p+12 } [/tex]
[tex]\\ \\ 7\left( p+12 \right) =9p\\ \\ 7p+84=9p\\ \\ 9p-7p=84\\ \\ 2p=84\\ \\ p=\frac { 84 }{ 2 } \\ \\ p=42[/tex]
Therefore:
[tex]\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { 42 }{ 42+12 } =\frac { 42 }{ 54 } =\frac { 7 }{ 9 } \cdot \frac { 6 }{ 6 } \\ \\ \therefore \quad n=6[/tex]
So all together there were 54 girls and 42 boys in the theatre.
54 + 42 = 96
That's 96 children in total. (Answer)
7:9 = 42:54
n is a number.
p is also a number, but different to n.
[tex]\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } \cdot 1=\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } =\frac { p }{ p+12 } [/tex]
[tex]\\ \\ 7\left( p+12 \right) =9p\\ \\ 7p+84=9p\\ \\ 9p-7p=84\\ \\ 2p=84\\ \\ p=\frac { 84 }{ 2 } \\ \\ p=42[/tex]
Therefore:
[tex]\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { 42 }{ 42+12 } =\frac { 42 }{ 54 } =\frac { 7 }{ 9 } \cdot \frac { 6 }{ 6 } \\ \\ \therefore \quad n=6[/tex]
So all together there were 54 girls and 42 boys in the theatre.
54 + 42 = 96
That's 96 children in total. (Answer)
7:9 = 42:54
