On an airplane that was 2/3 full, 20% of the passengers were boys, one-fourth of the passengers were women, one-eighth of the passengers were girls, and there were 51 men. How many seats are on the plane
the first thing you want to do is convert everything to either a fraction/ratio or a number
so it becomes
an airplane 2/3 full, 20% passengers were boys, 25% women, 12.5% girls, 51 men.
now, since you need 100%, you figure out what percent you have now: 20+25+12.5 = 57.5%
so 57.5% of the passengers WERE NOT men. That means that 42.5% WERE men. Since 42.5% were men, figure out how many passengers there are altogether. A percentage can become a decimal, e.g. 1% = .01; 42.5% = .425. Therefore, 42.5% of x = 51 becomes .425x=51. Solve for x and get 120. That means there were 120 total PASSENGERS on the plane. Since the plane is 2/3 full, do 2/3 y = 120. solve for y and get 180.
So there are 180 seats on the plane.
hope this helped you out.
You are completely right. (In my first post I made a very advantageous error so I got the correct final result) In short:
Let t denote the total number of seats and x the number of occupied seats. Then you have a system of simultaneous equations:
You'll get x = 120 and t = 180