3/4 of the students in a school were girls and the rest were boys. 2/3 of the firls and 12 of the boys attended the school carnvial. Find the toalt number of students in the school if 330 students did not attend the carnival
To find the total number of students in the school, we need to determine the number of students who attended the carnival and the number of students who did not.
Let's start by finding the number of girls who attended the carnival. We know that 2/3 of the girls attended the carnival. To determine the total number of girls in the school, we can assume that there are x girls. Therefore, the number of girls who attended the carnival is (2/3) * x.
Next, let's find the number of boys who attended the carnival. We know that 12 boys attended the carnival. Therefore, the number of boys in the school is 12.
Now, we can calculate the total number of students who attended the carnival by adding the number of girls and the number of boys: (2/3) * x + 12.
Since we are given that 330 students did not attend the carnival, we can subtract this number from the total number of students in the school. Therefore, the equation becomes:
Total number of students - Number of students who attended the carnival = 330.
Let's combine the information we have and set up the equation:
(3/4 * x) + 12 - (2/3 * x) = 330.
To simplify the equation, we need to find a common denominator:
(9/12 * x) + 12 - (8/12 * x) = 330.
Now, we can combine like terms:
(1/12 * x) + 12 = 330.
Subtracting 12 from both sides of the equation gives:
(1/12 * x) = 318.
To isolate x, we multiply both sides of the equation by 12:
x = 318 * 12.
Evaluating this expression gives:
x = 3816.
Therefore, the total number of students in the school is 3816.