Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Sagot :

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