A quantity T varies directly as the cube of m and inversely as n. If T = 54 when m = 3 and n = 2, find T when m = 2 and n = 4.

T = km³/n. Using T = 54, m = 3, n = 2: 54 = k × 27/2, so k = 54 × 2/27 = 4. When m = 2 and n = 4: T = 4 × 8/4 = 8. Distractors arise from errors in computing the constant or forgetting to cube m.