в) \( 1\frac{2}{3} \cdot (\frac{1}{3}n + \frac{3}{7}) = 2\frac{1}{4} \)

Решение:

1. \( \frac{5}{3} \cdot (\frac{1}{3}n + \frac{3}{7}) = \frac{9}{4} \)
2. \( \frac{1}{3}n + \frac{3}{7} = \frac{9}{4} : \frac{5}{3} \)
3. \( \frac{1}{3}n + \frac{3}{7} = \frac{9}{4} \cdot \frac{3}{5} \)
4. \( \frac{1}{3}n + \frac{3}{7} = \frac{27}{20} \)
5. \( \frac{1}{3}n = \frac{27}{20} - \frac{3}{7} \)
6. \( \frac{1}{3}n = \frac{189 - 60}{140} \)
7. \( \frac{1}{3}n = \frac{129}{140} \)
8. \( n = \frac{129}{140} \cdot 3 \)
9. \( n = \frac{387}{140} \)

Ответ: \( n = \frac{387}{140} \).