In a school, \(\frac{3}{4}\) of the students are girls, and the rest are boys. \(\frac{2}{3}\) of the girls and \(\frac{1}{2}\) of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.
Answer (2)
x − n u mb er o f b oys y − n u mb er o f g i r l s z − a ll s t u d e n t s y = 4 3 z x = 4 1 z 3 1 y + 2 1 x = 330 3 1 ( 4 3 z ) + 2 1 ( 4 1 z ) = 330 12 3 z + 8 1 z = 330 4 1 z + 8 1 z = 330 ∣ co mm o n d e n o mina t or 8 2 z + 8 1 z = 330 8 3 z = 330 ∣ m u lt i pl y b y 8 3 z = 2640 ∣ d i v i d e b y 3 z = 880 T o t a l n u mb er o f s t u d e n t s i s e q u a l t o 880.
The total number of students in the school is 880. This is calculated by determining the number of girls and boys, then using the attendance numbers for the carnival to find the total. The proportion of students who did not attend the carnival helped us set up the equation to solve for the total number of students.
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