In a furniture workshop the carpenters and the helpers are in the ratio 4 : 7, and the helpers and the apprentices are in the ratio 3 : 2. If there are 84 helpers, the workshop employs how many people in all?

Carpenters = $84\times 4/7=48$ and apprentices = $84\times 2/3=56$, so the workshop has 48 + 84 + 56 = 188 people. (Stringing the given numbers together as 4 : 7 : 2 gives 24 apprentices and a total of 156 — the two ratios must first be put on a common value of the helpers, which is 84 itself here. 132 leaves the apprentices out and 140 leaves the carpenters out.)