The table below shows the number of males working in private and public companies and the number of females working in private and public companies in four different cities (A, B, C & D).

| City | Males in Private Company | Males in Public Company | Females (Private + Public) |
|-------|--------------------------|-------------------------|----------------------------|
| A | $15x - 2y$ | $y$ | 55 |
| B | $16x$ | 16 | 108 |
| C | $9y$ | 24 | 74 |
| D | 84 | 21 | 85 |

Additional information:

1. Number of male employees in city A is 50.
2. Total males working in private companies from cities B and C is 154.
3. Total employees (male + female) working in any city = employees in private companies + employees in public companies.
4. Total males/females working in any city = sum of males/females working in private and public companies.
5. 50% of the total females from all cities work in private companies.

**Question:** Find the total number of employees (male + female) working in public companies from all the cities combined.

Question

The table below shows the number of males working in private and public companies and the number of females working in private and public companies in four different cities (A, B, C & D).

| City | Males in Private Company | Males in Public Company | Females (Private + Public) |
|-------|--------------------------|-------------------------|----------------------------|
| A     | $15x - 2y$               | $y$                     | 55                         |
| B     | $16x$                    | 16                      | 108                        |
| C     | $9y$                     | 24                      | 74                         |
| D     | 84                       | 21                      | 85                         |

Additional information:

1. Number of male employees in city A is 50.
2. Total males working in private companies from cities B and C is 154.
3. Total employees (male + female) working in any city = employees in private companies + employees in public companies.
4. Total males/females working in any city = sum of males/females working in private and public companies.
5. 50% of the total females from all cities work in private companies.

**Question:** Find the total number of employees (male + female) working in public companies from all the cities combined.

Accepted Answer

**Solution:**

1. Calculate the total number of females from all cities:
   $$55 + 108 + 74 + 85 = 322$$

2. Since 50% of the total females work in private companies, the remaining 50% work in public companies:
   $$	ext{Females in public companies} = 50\% 	imes 322 = 161$$

3. Calculate total males working in public companies from all cities:
   - From city A: males in public company = $y$
   - From city B: males in public company = 16
   - From city C: males in public company = 24
   - From city D: males in public company = 21

4. Use the given information to find $x$ and $y$:
   - Number of males in city A = 50:
     $$15x - 2y + y = 50 \implies 15x - y = 50$$

- Total males working in private companies from cities B and C = 154:
     $$16x + 9y = 154$$

5. Solve the system of equations:
   From equation 1:
   $$y = 15x - 50$$

Substitute into equation 2:
   $$16x + 9(15x - 50) = 154$$
   $$16x + 135x - 450 = 154$$
   $$151x = 604$$
   $$x = \frac{604}{151} = 4$$

Then,
   $$y = 15 	imes 4 - 50 = 60 - 50 = 10$$

6. Calculate males in public companies from all cities:
   $$y + 16 + 24 + 21 = 10 + 16 + 24 + 21 = 71$$

7. Total employees working in public companies = females in public companies + males in public companies:
   $$161 + 71 = 232$$

**Answer:** 232

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