ecm brainbuster no. 40 - bonus time

The brainbuster

A successful company has 100 staff, each of which is to receive a bonus. The bonus pool is 200k. Senior staff will get 6k each, mid-level staff 4k each, and junior staff 1k each. Given that there are five times as many mid-level as senior staff, how many staff are there in each group?

Show your workings. Only complete entry forms will be considered. The judge's decision is final.

The entries

As mentioned, not such a challenge this time round, but still enough of a problem to trip up some entrants! Well done to all who worked out the right answer.

The solution

A straightforward problem of simultaneous equations. As expressed by one winner:

Senior Staff (S): 5
Mid level Staff (M): 25
Junior Staff (J): 70

It's a simultaneous equations problem:
    (1) S + M + J=100
    (2) 6S + 4M + J=200

Using M = 5S can get J = 100 - 1.2M from (1)

And using these in (2) gives M=25 which allows us to find S=5 and J=70.

And the winners are...

The winners of ecm's brainbuster no. 40 are Stuart Lane, Elliott Levi, Jack McKenzie and Angus Maidment.

Each wins £50 of Amazon vouchers to spend on high-tech.

Congratulations again to our winners, and watch out for ecm's next brainbuster!