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# At a certain restaurant, the average (arithmetic mean) number of custo

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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21 Aug 2015, 04:15
1
3
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:20) correct 14% (02:02) wrong based on 128 sessions

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At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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21 Aug 2015, 04:20
1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

Per the question,

$$\frac{75x+120}{x+1}$$ =90 ---> x =2. A is the correct answer.
Director
Joined: 21 May 2013
Posts: 652
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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21 Aug 2015, 05:14
1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

No of customers/No of days=75
C/x=75
C=75x
Now, C+120/x+1=90
Put C=75x from the earlier equation,
15x=30
x=2
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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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21 Aug 2015, 20:13
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Ans: A
Solution: from the given info we can say if N is the total number of people served in x says then avg 75=N/x = N=75x
and after todayavg 90= (N+120)/(x+1); puttine the value of N we get the x=2
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Joined: 23 Jan 2013
Posts: 568
Schools: Cambridge'16
At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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21 Aug 2015, 22:11
1
Algebraic:

y/x=75
(y+120)/(x+1)=90
75x+120=90x+90
30=15x => x=2

Backsolving:

take 9 (C) 75*9=675+120=795/10=79.5, too low average so should take less days
take 5 (B) 75*5=375+120=495/6=82.5, low again but going up, so must be 2

A
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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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22 Aug 2015, 00:09
1
Equating total number of customers served
75x+120 = 90(x+1)
=> 15x = 30
x=2

Manager
Joined: 06 Jan 2014
Posts: 60
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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23 Aug 2015, 02:20
1
Total Customers Served in X days = 75x

Total customers served after today 75x+120

New Average (75x+120)/x+1 = 90

Solving X =2 ( Option A)
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Manager
Joined: 10 Jun 2015
Posts: 118
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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23 Aug 2015, 03:40
1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

the increase in average is 15
the increase in customers from the mean is 45
45/15 = 3 is x+1
Therefore, x=2
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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23 Aug 2015, 11:22
1
1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

WITHOUT using the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the “deficit” below the average of 90 created on the x days the restaurant served only 75 customers per day.

30/15 = 2 days. Choice (A).

WITH the formula, we can set up the following:

90 = (75x + 120)/(x + 1)

90x + 90 = 75x + 120

15x = 30

x = 2 Answer Choice (A)

Use whichever makes more sense to you!
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Intern
Joined: 30 Sep 2013
Posts: 20
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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24 Aug 2015, 08:18
HI Bunnel,

If you could you explain more elaborately, that would be very helpful.
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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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24 Aug 2015, 17:20
riteshgmat wrote:
HI Bunnel,

If you could you explain more elaborately, that would be very helpful.

Hi riteshgmat

Perhaps I can be of assistance. He means, whatever the residual is, it must be spread across the days equally, one part below and another above. The residual here is 30 days ($$120 - 90 = 30$$) and so to have the new average be 90, it must have been split into two $$15$$s and therefore, the number of days is $$2$$.

Kr,
Ron
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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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16 Dec 2016, 16:03
Nice Question
Here is my solution to this one =>

$$Using Mean = \frac{Sum}{#}$$

Sum(x)=75x

Sum(x+1)=75x+120

As pre Question => 75x+120/x+1=90
Hence x=2

Alternately,
75+15(x+1)=120
x=2

Hence A

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Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

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05 Oct 2018, 04:06
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