Question

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

Answer 1

`x-\ number\ of\ boys\\\\y-\ number\ of\ girls\\\\ z-\ all\ students\\\\ y=(3)/(4)z\\ x=(1)/(4)z\\\\ (1)/(3)y+(1)/(2)x=330\\\\ (1)/(3)((3)/(4)z)+(1)/(2)((1)/(4)z)=330\\\\ (3)/(12)z+(1)/(8)z=330\\\\ (1)/(4)z+(1)/(8)z=330\ \ \ | common\ denominator\\\\ (2)/(8)z+(1)/(8)z=330\\\\ (3)/(8)z=330\ \ \ | multiply\ by\ 8\\\\ 3z=2640\ \ \ | divide\ by\ 3\\\\z=880\\\\ Total\ number\ of\ students\ is\ equal\ to\ 880.`