the ratio of men and women in a certain factory is 3 to 4. there are 198 men. How many workers are there?

3 men

4 women

7 total

3 men / 7 total = 198 men / x total

using cross products

3*x = 7 * 198

divide each side by 3

x = 7*198/3

x = 462

There are 462 workers

If you mean 3 men and 1 women for a total of 4 workers when you state a ratio of men and women in a certain factory is 3 to 4.

3/4 = 198/x

Using cross products

3x = 4 * 198

Divide each side by 3

3x/3 = 4*198/3

x = 264

264 workers

It all depends on how you define ratio of men and women in a certain factory is 3 to 4. This is incorrect phrasing and I took it to be men to women. You cannot have a ratio of men and women.