In an office there are twice as many females as males. 1/4 of the females wear glasses. 3/8 of the males wear glasses. 84 people in the office wear glasses. Work out the number of people in the office.

office that is females with glasses=(2/3)(1/4)=1/6 office that is males wearing glasses=(1/3)(3/8)=1/8 (1/6)/(1/8) = 8/6=4/3 so there is a ratio of 4:3 women to men wearing glasses 84*(4/7)=124=48 women with glasses 448 = 192 women total 84*(3/7)=12*3=36 men with glasses (8/3)*36=96 men total so total of 192+96=288 people in the office (checks: 192/96=2 so twice as many females as males, 288/36=1/8 so correct ratio of males,. 288/48=1/6 so correct ratio of females)