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# The wait time in minutes, w, for a table at a certain restaurant can

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Math Expert
Joined: 02 Sep 2009
Posts: 56277
The wait time in minutes, w, for a table at a certain restaurant can  [#permalink]

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31 Jul 2018, 00:49
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Difficulty:

5% (low)

Question Stats:

92% (01:57) correct 8% (01:18) wrong based on 29 sessions

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The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula $$w = d^2 + kn$$, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?

(A) 28
(B) 33
(C) 39
(D) 42
(E) 48

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Re: The wait time in minutes, w, for a table at a certain restaurant can  [#permalink]

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31 Jul 2018, 01:06
Bunuel wrote:
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula $$w = d^2 + kn$$, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?

(A) 28
(B) 33
(C) 39
(D) 42
(E) 48

As the calculation we're asked to do is straightforward, we'll just do it.
This is a Precise approach.

We're told that when d = 4 and n = 6 then w = 40
Plugging this in gives 40 = 4^2 +6k --> k = 4

So, if d = 6 and n = 3, then w = 6^2 + 3*4 = 48

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Re: The wait time in minutes, w, for a table at a certain restaurant can  [#permalink]

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31 Jul 2018, 03:27
Bunuel wrote:
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula $$w = d^2 + kn$$, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?

w = d^2 + kn
d = 4, n = 6, w = 40
On solving we get,
40 = 4^2 +6k
40 = 16 + 6k
6k = 24
k = 4

Again, for second case
d = 6, n = 3, k = 4
w = 6^2 + 3*4
w = 36 + 12
w = 48

Hence, E.
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Re: The wait time in minutes, w, for a table at a certain restaurant can  [#permalink]

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10 Aug 2018, 19:13
Bunuel wrote:
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula $$w = d^2 + kn$$, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?

(A) 28
(B) 33
(C) 39
(D) 42
(E) 48

We are given that a party of 4 has a wait time of 40 minutes when 6 other parties are ahead of it. We can use this information to determine the value of k in the following equation:

40 = 4^2 + k(6)

40 = 16 + 6k

24 = 6k

4 = k

Now, we can find the wait time of a party of 6 when there are 3 parties ahead of it:

w = 6^2 + 4(3) = 36 + 12 = 48

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Re: The wait time in minutes, w, for a table at a certain restaurant can   [#permalink] 10 Aug 2018, 19:13
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