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

Question

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.

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

Kudos for a correct  solution .

ENGRTOMBA2018 · Answer

Per the question,

\frac{75x+120}{x+1}  =90 ---> x =2. A is the correct answer.

KS15 · Answer

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
Answer A

D3N0 · Answer

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

Temurkhon · Answer

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

akhilbajaj · Answer

Equating total number of customers served
75x+120 = 90(x+1)
=> 15x = 30
x=2

Answer A.

dream21 · Answer

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)

mathivanan · Answer

the increase in average is 15
the increase in customers from the mean is 45
45/15 = 3 is x+1
Therefore, x=2

Bunuel · Answer

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!

riteshgmat · Answer

HI Bunnel,

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

mejia401 · Answer

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

stonecold · Answer

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

bumpbot · Answer

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

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