Question

In a recent study of a bee hive, it was found that there were a total of 4,109 bees, not including the queen. There were thirty‑three more nurses than drones. The number of workers was twelve more than six times the number of drones. How many of each type of bee were in the hive?

Answer 1

There were 508 drones, 541 nurses and 3060 workers.

Explanation:

Total number of bees = 4109

Let the number of drones, nurses and workers be represented by x, N and W respectively.

But,

N = x + 33 .......... 1

W = 6x + 12 .......... 2

So that,

x + (x + 33) + (6x + 12) = 4109

x + x + 33 + 6x + 12 = 4109

8x + 45 = 4109

8x = 4064

x =
`(4064)/(8)`

= 508

x = 508

From equation 1,

N = 508 + 33

= 541

N = 541

From equation 2,

W = 6x + 12

= 6(508) + 12

= 3060

W = 3060

= 3060

In the hive, there were 508 drones, 541 nurses and 3060 workers.