In company F, the ratio of total male managers to total female managers is $7 : 2$. Given that the percentage of managers out of total employees in company F is $18\%$ and the number of female managers is $18$, find the total number of non-manager employees in company F.

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**Solution:**

1. Let the total number of employees in company F be $100x$.

2. Since $18\%$ of employees are managers, total managers = $18\%$ of $100x = 18x$.

3. The ratio of male to female managers is $7 : 2$. Let the common multiplier be $u$.

- Female managers = $2u$
   - Male managers = $7u$

4. Given female managers = 18, so:
   $$2u = 18 \implies u = 9$$

5. Total managers = $7u + 2u = 9u = 9 	imes 9 = 81$.

6. Equate total managers calculated from percentage and ratio:
   $$18x = 81 \implies x = \frac{81}{18} = 4.5$$

7. Total non-manager employees = Total employees - Managers
   $$= 100x - 18x = 82x = 82 	imes 4.5 = 369$$

**Answer:** $369$

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