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

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