3/4 of the students in a school were girls and the rest were boys. 2/3 of the girls and 1/2 of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.

g = 3b, since 3/4 = 3 * 1/4

2/3 g + 1/2 b attended
2/3 (3b) + 1/2 b = 5/2 b attended

subtract that from the total (b+g) students:

b+g - 5/2 b = 330
4b - 5/2 b = 330
3/2 b = 330
b = 220
so, g = 660

There are 880 students
660 girls and 220 boys

440 girls and 110 boys attended: 550
the remaining 330 did not attend.

Nice twist to an otherwise common exercise.

I got 250, That is a much more resonable answer

The actual answer is 880 students. I checked with my teacher.

since you add the 330 to the 550

so HAH! I beat you!!!!

250 boys

To find the total number of students in the school, we can start by finding the number of students who attended the carnival.

Let's denote the total number of students in the school as "x."
Given that 3/4 of the students were girls and the rest were boys, we can calculate the number of girls and boys.
Number of girls = 3/4 * x
Number of boys = 1/4 * x

Next, we are told that 2/3 of the girls and 1/2 of the boys attended the carnival. Therefore,
Number of girls who attended the carnival = 2/3 * (3/4 * x) = 2/3 * 3/4 * x = 1/2 * x
Number of boys who attended the carnival = 1/2 * (1/4 * x) = 1/2 * 1/4 * x = 1/8 * x

The total number of students who attended the carnival is the sum of the number of girls and the number of boys:
Number of students who attended the carnival = Number of girls who attended + Number of boys who attended
= 1/2 * x + 1/8 * x
= 4/8 * x + 1/8 * x
= 5/8 * x

We are also given that 330 students did not attend the carnival. Therefore, the number of students who attended the carnival must be the total number of students minus the number of students who did not attend:
Number of students who attended the carnival = Total number of students - Number of students who did not attend
= x - 330

Since we know that the number of students who attended the carnival is equal to 5/8 of the total number of students, we can set up an equation:
5/8 * x = x - 330

We can solve this equation to find the value of x, which represents the total number of students in the school.

Multiply both sides of the equation by 8 to eliminate the fraction:
5x = 8(x - 330)

Expanding the equation:
5x = 8x - 2640

Subtracting 8x from both sides:
-3x = -2640

Dividing both sides by -3:
x = -2640 / -3

Simplifying:
x = 880

Therefore, the total number of students in the school is 880.