SOLUTION: 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 in the theater. How many children are in the theater.

Question 1130340: 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 in the theater. How many children are in the theater.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let b number of boys.
let g = number of girls.

ratio of boys to girls is 7:9.

equation for that is b/g = 7/9

in the theater, there are 12 more girls than boys.

equation for that is g = b + 12

these two equations need to be solved simultaneously.

they are:

b/g = 7/9
g = b + 12

in the first equation, replace g with b + 12 from the second equation to get:

b/(b + 12) = 7/9

cross multiply to get 9b = 7 * (b + 12)

simplify to get 9b = 7b + 84

subtract 7b from both sides of the equation to get 2b = 84

solve for b to get b = 42

since g = b + 12, then g = 54.

the number of boys in the theater is 42 and the number of girls in the theater is 54.

the number of children in the theater is 42 + 54 = 96

the ratio of boys to girls in the theater is 42 / 54.

divide numerator and denominator by 6 to get the ratio of boys to girls in the theater is 7 / 9.

54 - 42 = 12 which means there are 12 more girls in the theater than boys.

your solution is that the number of children in the theater is 96.

since the ratio of boys to girls is 7 / 9, this means that, out of every 15 students, 7 are boys and 9 are girls.

the ratio of boys to total children in the theater is therefore 7 / 15.

the ratio of girls to total children in the theater is therefore 9 / 15.

7/15 * 96 = 42.

9/15 * 96 = 54.

it all checks out, so the solution is assumed to be good.

solution is 96 children in the theater.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
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 in the theater. How many children are in the theater.

Let the multiplicative factor be x
Then number of boys and girls are 7x, and 9x, respectively
As given, 7x = 9x - 12
7x - 9x = - 12
- 2x = - 12

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