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# A theater box office sold an average of 65 tickets per staff

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A theater box office sold an average of 65 tickets per staff [#permalink]

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08 Jul 2014, 07:29
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88% (01:23) correct 12% (02:36) wrong based on 99 sessions

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A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 76, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?

A) 1:1
B) 1:4
C) 5:11
D) 7:11
E) 65:76
[Reveal] Spoiler: OA

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Re: A theater box office sold an average of 65 tickets per staff [#permalink]

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08 Jul 2014, 08:12
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Gnpth wrote:
A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 76, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?

A) 1:1
B) 1:4
C) 5:11
D) 7:11
E) 65:76

Deviation from the mean for the daytime staff = 76 - 65 = 11.
Deviation from the mean for the evening staff = 65 - 60 = 5.

Thus, the ratio of the number of daytime staff members to the number of evening staff members = 5:11.

Or: (76x + 60y)/(x + y) = 65 --> x/y = 5/11.

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A theater box office sold an average of 65 tickets per staff [#permalink]

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08 Jul 2014, 20:58
Let "d" is the total no. of day staff

So, total collection in day = 76d .............. (1)

Let "n" is the total no. of night staff

So, total collection in night = 60n ................. (2)

Total Day & Night staff = (d+n) & overall average = 65

So, total collection (Day & Night) = 65(d+n) ........... (3)

(1) + (2) = (3)

76d + 60n = 65d + 65n

11d = 5n

$$\frac{d}{n} = \frac{5}{11}$$

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Re: A theater box office sold an average of 65 tickets per staff [#permalink]

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08 Jul 2014, 21:13
One more method:

Using allegation

Refer diagram below:
Attachments

ja.jpg [ 11.43 KiB | Viewed 1455 times ]

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Re: A theater box office sold an average of 65 tickets per staff [#permalink]

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20 Sep 2017, 10:18
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Re: A theater box office sold an average of 65 tickets per staff [#permalink]

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25 Sep 2017, 17:58
Gnpth wrote:
A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 76, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?

A) 1:1
B) 1:4
C) 5:11
D) 7:11
E) 65:76

We can let d = the number of daytime staff and e = the number of evening staff, and thus:

65 = (76d + 60e)/(d + e)

65d + 65e = 76d + 60e

5e = 11d

5/11 = d/e

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Re: A theater box office sold an average of 65 tickets per staff   [#permalink] 25 Sep 2017, 17:58
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