Question

The ratio of the number of boys to the number of girls in a theater is 7:9. There are 12 more girls than boys. How many children are in the theater

Answer 1

Ok, there is an equation you can use to solve it.

n is a number.

p is also a number, but different to n.

$\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } \cdot 1=\frac { p }{ p+12 } \\ \\ \frac { 7 }{ 9 } =\frac { p }{ p+12 }$

$\\ \\ 7\left( p+12 \right) =9p\\ \\ 7p+84=9p\\ \\ 9p-7p=84\\ \\ 2p=84\\ \\ p=\frac { 84 }{ 2 } \\ \\ p=42$

Therefore:

$\frac { 7 }{ 9 } \cdot \frac { n }{ n } =\frac { 42 }{ 42+12 } =\frac { 42 }{ 54 } =\frac { 7 }{ 9 } \cdot \frac { 6 }{ 6 } \\ \\ \therefore \quad n=6$

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