Problem Solving

BlueDragon2010 wrote:A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

A) 3
B) 10
C) 25
D) 30
E) 35

A factory has 500 workers, 15 percent of whom are women
15% of 500 = 75
So, there are presently 75 women at the factory


Once the additional 50 workers are hired, there will be 550 workers.
We want 20% of those 550 workers to be women.
20% of 550 = 110, so we need there to be 110 women altogether.

So, we need to increase the number of female workers from 75 to 110.
110 - 75 = 35

So, 35 of the additional workers must be women.

Answer: E

Cheers,
Brent

BlueDragon2010 wrote:A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

A) 3

B) 10

C) 25

D) 30

E) 35

Solution:

Let's first determine the number of women currently working at the factory. We know that there are 500 workers, and 15% of them are women. Thus, we know there are:

500 x 0.15 = 75 women

We are asked, if 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent? To translate this idea into a mathematical statement, we have:

(Number of women after hire)/(total workers after hire) = 20%

To solve this statement, we can set up the actual equation with the numbers given from the question stem, and we can let w be the number of additional women hired:

(75 + w)/(500 + 50) = 20%

(75 + w)/550 = 0.2

75 + w = 550 x 0.2

75 + w = 110

w = 35

Answer:E