Carcass wrote:
A company employs 20 workers for every 3 managers, and 5 managers for every director. If the total number of employees at the company is between 300 and 400, what is the number of managers who work at the company?
enter your valueLet
W = # of workersLet
M = # of managersLet
D = # of directorsCompany employs 20 workers for every 3 managersSo,
W :
M =
20 :
3Company employs 5 managers for every 1 directorSo,
M:
D =
5:
1The common value is
the number of managers. So, let's create some
EQUIVALENT ratios so that both ratios have the same
number of managers.
Take
20 :
3 and multiply both values by 5 to get:
100 :
15Take
5:
1 and multiply both values by 3 to get:
15:
3We can now COMBINE the ratios to get:
W :
M :
D =
100 :
15 :
3So, one POSSIBLE scenario is that there are
100 workers,
15 managers, and
3 directors for a TOTAL of 118 people.
Another POSSIBLE scenario is that there are
200 workers,
30 managers, and
6 directors for a TOTAL of 236 people.
Another POSSIBLE scenario is that there are
300 workers,
45 managers, and
9 directors for a TOTAL of 354 people. PERFECT!!
We're told that the total number of employees at the company is between 300 and 400.
So, the last scenario meets this condition.
So, there must be
45 managers
Answer: 45