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?
b/g = 7/9
g-12 = b
so
(g-12)/g = 7/9
9(g-12) = 7g
2 g = 108
g = 54
b = 42
sum = 96
This isnt helpful at all, i need the answer without letters in the numbers!
To solve this question, we can set up a system of equations.
Let's assume the number of boys in the theater is 7x, and the number of girls is 9x.
According to the problem, there are 12 more girls than boys. So we can write an equation:
9x = 7x + 12
Simplifying the equation:
9x - 7x = 12
2x = 12
x = 12/2
x = 6
Now we can substitute the value of x back into the original expressions to find the total number of children in the theater:
Number of boys = 7x = 7 * 6 = 42
Number of girls = 9x = 9 * 6 = 54
Total number of children in the theater = Number of boys + Number of girls = 42 + 54 = 96
Therefore, there are 96 children in the theater.
To solve this problem, we will set up a system of equations to represent the given information.
Let's assume the number of boys in the theater is B and the number of girls is G.
From the given information, we know that the ratio of boys to girls is 7:9, which means B/G = 7/9.
We also know that there are 12 more girls than boys, so we can write another equation as G = B + 12.
Now we can solve this system of equations to find the values of B and G.
First, let's substitute the value of G from the second equation into the first equation:
B / (B + 12) = 7 / 9
Cross-multiplying gives us:
9B = 7(B + 12)
Expanding the equation gives us:
9B = 7B + 84
Subtracting 7B from both sides gives us:
2B = 84
Dividing both sides by 2 gives us:
B = 42
Now that we have the value of B, we can substitute it into the second equation to find the value of G:
G = B + 12
G = 42 + 12
G = 54
Therefore, the number of boys in the theater is 42 and the number of girls is 54. The total number of children in the theater is the sum of the boys and girls:
Total number of children = 42 + 54 = 96
So, there are 96 children in the theater.