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

Let's figure out what information we have and let's translate it into mathematical terms.
Let f = number of females in the office m=number of males in the office
"Twice as many females than males" translates to : f = 2m (1)"1/4 of the females wear glasses" translates to : # of females wearing glasses = 1/4 fSimilary, "3/8 of the males wear glasses" means : # of males wearing glasses = 3/8 m"84 people in the office wear glasses" is : 84= (# of females wearing glasses) + (# of males wearing glasses) = 1/4 f + 3/8 m (2)
Let's figure out what is the question asking, in mathematical terms.
"Number of people in the office" means : # people in the office = f + m = ??
We now have everything we need to solve the equation! Indeed we sub (1) into (2) : 1/4 (2m) + 3/8 m = 84 <=> 1/2 m + 3/8 m = 84 <=> 4/8 m + 3/8 m = 84 <=> 7/8 m = 84 <=> m = 84 x 8/7 <=> m = 12 x 8 <=> m = 96 . Now let's sub the result in (1) : f = 2 m = 2 x 96 = 192.
Therefore the solution of the problem is : f + m = 96 + 192 = 288 .