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An office building housed some tenants and service workers.

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An office building housed some tenants and service workers.  [#permalink]

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New post 30 Sep 2019, 10:32
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Difficulty:

  55% (hard)

Question Stats:

60% (02:37) correct 40% (03:07) wrong based on 42 sessions

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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
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Re: An office building housed some tenants and service workers.  [#permalink]

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New post 30 Sep 2019, 12:06
Hovkial wrote:
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


Tenants ———— workers
— t ———————w——

15 workers left the building
— t —————— w-15 —
This left two tenants for each worker. —> t = 2(w-15)
—2(w-15)————w-15 —
Subsequently, forty-five tenants left.
—2(w-15)-45 —— w-15 —
Now there were five workers left for each tenant.
—> 5(2(w-15) - 45) = (w-15)
—> 10w - 375 = w - 15
—> 9w = 360
—> w = 40

IMO Option C

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Re: An office building housed some tenants and service workers.  [#permalink]

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New post 05 Oct 2019, 16:50
Hovkial wrote:
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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Re: An office building housed some tenants and service workers.   [#permalink] 05 Oct 2019, 16:50
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