Final answer:
After setting up a ratio equation with men represented as 7x and women as 5x and knowing the total number of employees is 312, you solve for the value of x to find out that there are 130 women working for the company.
Step-by-step explanation:
To find out how many women work for the company when the ratio of men to women working for the company is 7 to 5 and there are 312 employees total, one must set up a ratio equation and solve for the number of women.
Let the number of men be represented by 7x and the number of women by 5x. The total number of employees is the sum of the men and women, which we know is 312.
So, the equation becomes:
7x + 5x = 312
Combine the like terms to find the total number of 'parts' the company employees are divided into:
12x = 312
To find the value of x, divide both sides of the equation by 12:
x = 312 / 12
x = 26
Now, to find the number of women, multiply the number of 'women parts' by x:
5x = 5 × 26
5x = 130
Therefore, there are 130 women working for the company.