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
