Managers to Workers - Ratios

EricKryk wrote:In a certain company, the ratio of the number of managers to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A) 5
B) 10
C) 15
D) 20
E) 25

Another option is to use TWO VARIABLES

Let M = CURRENT # of managers
Let W = CURRENT # of production-line workers

The ratio of the number of managers to the number of production-line workers is 5 to 72.
So, we can write: M/W = 5/72
Cross multiply to get: 5W = 72M

If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74
If 8 workers are hired then:
W + 8 = NEW number of workers
Also, M = number of managers (since nothing changes with the managers).
We can now write: M/(W + 8) = 5/74
Cross multiply to get: 74M = 5(W + 8)
Expand: 74M = 5W + 40
Rearrange to get: 74M - 40 = 5W

So, we now have two equations: 5W = 72M and 74M - 40 = 5W

Since BOTH equations are set equal to 5W, we can conclude that 72M = 74M - 40
Subtract 74M from both sides to get: -2M = -40
Solve to get M = 20

So, there are 20 managers.

Answer: D

Cheers,
Brent

Hi EricKryk,

Since the other explanations have focused more on the algebra behind this prompt, here's another approach: TEST THE ANSWERS:

We'll start with answer B, which is 10 managers…

To start, we have a ratio of 5 managers to 72 workers, so….
10 managers & 144 workers
Then we're told to +8 workers

Now we have…
10 managers & 152 workers
This ratios is…5:76 which is not a match for what we're looking for (we want 5:74, so we'll need more managers)

Next, try answer D, which is 20 managers….

20 managers & 288 workers
Now +8 workers gives us….

20 managers & 296 workers
This ratio is 5:74 which is a MATCH for what we're looking for.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

EricKryk wrote:In a certain company, the ratio of the number of managers to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A) 5
B) 10
C) 15
D) 20
E) 25

We are given that the ratio of managers to production-line workers is 5 to 72, or 5x to 72x. We can create the following equation:

(5x)/(72x + 8) = 5/74

74(5x) = (72x + 8)(5)

370x = 360x + 40

10x = 40

x = 4

The company has 4 x 5 = 20 managers.

Answer: D