Answered

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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
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