The sum of four consecutive odd numbers is L and their average is M; the sum of three consecutive even numbers is P and their average is Q, with P = L - 16 and Q = M + 6. Find M.

M = 34.

Four consecutive odd numbers give sum L = 4M.

Three consecutive even numbers give sum P = 3Q.

Use P = L - 16 and Q = M + 6: 3(M + 6) = 4M - 16.

3M + 18 = 4M - 16 gives M = 34.

Here sum = count x average for each set.