An office building housed some tenants and service workers. In a certain month, 15 workers left the building. This left two tenants for each worker. Subsequently, forty-five tenants left. Now there were five workers left for each tenant. How many service workers lived in the building at the beginning?

(A) 30

(B) 35

(C) 40

(D) 45

(E) 50

We can let t = the number of tenants and s = the number of service workers. After the first action, in which 15 workers left, the number of tenants was unchanged. There were now (s - 15) service workers, and this was half the number of tenants. We can create the equation:

1/2t = (s - 15)

t = 2(s - 15)

After the second action, the number of service workers was still (s - 15), but 45 tenants had left, so we have (t - 45). The new relationship between the two groups was that there were now 5 times as many workers as tenants, so we have:

s - 15 = 5(t - 45)

Substituting 5(t - 45) for s - 15 in the first equation, we have:

t = 2(5(t - 45))

t = 10t - 450

450 = 9t

50 = t

Now, substituting 50 for t in the first equation, we have:

50 = 2(s - 15)

25 = s - 15

40 = s

Answer: C
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