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 carnivel. Find the total number of students in the school if 330 students did not attend the carnivel.
what have they told you? If there are x students, then
g = 3/4 x
b = 1/4 x
1/3 g + 1/2 b = x-330
substituting for b and g,
1/3 * 3/4 x + 1/2 * 1/4 x = x - 330
...
To find the total number of students in the school, we need to break down the information given and work step by step.
Let's assume the total number of students in the school is represented by "x."
Given that 3/4 of the students were girls, we know that there were (3/4)x girls in the school.
The remaining students must be boys, so the number of boys in the school is (1/4)x.
Now, it is given that 2/3 of the girls attended the carnival, so the number of girls who attended the carnival is (2/3)(3/4)x.
Similarly, 1/2 of the boys attended the carnival, so the number of boys who attended the carnival is (1/2)(1/4)x.
We are given that 330 students did not attend the carnival, so we subtract the number of students who attended (girls and boys) from the total number of students.
Thus, we can set up the equation:
x - [(2/3)(3/4)x + (1/2)(1/4)x ] = 330
To solve this equation:
First, simplify the equation:
x - [(2/3)(3/4)x + (1/2)(1/4)x ] = 330
x - [(6/12)x + (1/8)x] = 330
x - [(6/12 + 1/8)x] = 330
Now, let's find a common denominator for the fractions:
x - [(6/12 + 3/24)x] = 330
x - [(12/24 + 3/24)x] = 330
x - [(15/24)x] = 330
Combine like terms:
x - (15/24)x = 330
(24/24)x - (15/24)x = 330
(9/24)x = 330
Simplify the equation further:
(9/24)x = 330
(3/8)x = 330
To isolate x, multiply both sides of the equation by the reciprocal of (3/8), which is (8/3):
(3/8)x * (8/3) = 330 * (8/3)
x = 1320
Therefore, the total number of students in the school is 1320.