A universal​ set, with​ n(U) = 168​, is partitioned into three​ subsets: A,​ B, and C. If​ n(B) = 5​⋅n(A), and​ n(C) = 3​⋅n(B), find n(A).

Question

A universal set, with n(U) = 168, is partitioned into three subsets: A, B, and C.  
If n(B) = 5⋅n(A), and n(C) = 3⋅n(B), find the number of elements in the subset A.

Answer 1

n(U) =168

A+B +C = 168

B=5A

C=3B=3(5B) = 15A

A+5A +15A = 168

21A =168

A=168/21 =8

n(A)=8

n(B)=40

n(C)=120