The Foreman was back in the Site Manager's office with another demand from the bricklayers.
Only four weeks ago they had held a working practices meeting and told the Foreman that they would be reducing the daily output for each bricklayer by 100 bricks. The Site Manager could not allow the overall number of bricks laid each day to drop, as the project would not be completed on time, and he had had to hire two more bricklayers to keep up the required rate.
As before, the bricklayers were reducing the number of bricks laid by each bricklayer each day by 100.
The Site Manager was furious, as this drop in productivity by 200 bricks per bricklayer per day from the start of the build was severely threatening his reputation. But he had to finish on schedule and so he asked the Foreman to hire a further two bricklayers.
"Unfortunately, that will not be enough this time." replied the Foreman, "To keep up the required building rate we will have to engage three more bricklayers."
How many bricklayers laying how many bricks per day were there at the start of the build?
Let n be the number of bricklayers and b the daily output per bricklayer per day at the project start.
Given the 100-brick per day reduction was made up by two more bricklayers:
nb = (n + 2)(b - 100) = nb - 100n + 2b -200
and rearranging gives
0 = 2b -100n - 200 [1]
Then from the second 100-brick per day reduction being made up by three extra bricklayers:
(n + 2)(b - 100) = (n + 5)(b - 200)
and a similar rearrangement gives
0 = 3b - 100n - 800 [2]
Subtracting equation 1 from equation 2 gives
0 = b - 600
And so the original number of bricks per bricklayer per day is 600.
Putting this back into equation 1 gives
0 = 1200 - 100n -200
So
100n = 1000
And the original number of bricklayers was 10.