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02 May 2012, 15:55
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Difficulty:

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Question Stats:

65% (01:31) correct 35% (01:39) wrong based on 1523 sessions

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The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? (A)$11.73
(B) $12.00 (C)$13.80
(D) $14.00 (E)$15.87

[Reveal] Spoiler:
How come the answer is B?

This is how I solved it and got A, which is incorrect.

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03 May 2012, 07:51
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enigma123 wrote:
The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? A. 11.73 B. 12 C. 13.8 D. 14 E. 15.87 How come the answer is B? This is how I solved it and got A, which is incorrect.$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73

I'll show You perhaps the most easiest way to solve such problem

As it is a percentage problem so just take the initial price before the gratuity is 100 the as the gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 207 is for 115 then we have to calculate for 100 here we go

for 115 207
for 100 x

so by cross multiplication we get 115x=100*207 => x=100*207/110 by simplifying we get x as 180 which is the price of lunch before gratuity so the gratuity is 27 so

as the question ask the average price person excluding gratuity is 180/15=12 so our answer is b

hope its concise and clear .

if u satisfied with my effort don't hesitate to give +1 kudos.

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03 May 2012, 12:56
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kashishh wrote:
GyanOne wrote:
The mistake you have made is that you have calculated the gratuity on the final amount, instead of finding the amount on which gratuity was charged to get the final amount.

If the amount spent excluding the gratuity was x, then x(1.15) = 207
=> x = 207/1.15 = 180

Then the average price per person = 180/15 = 12

Option (B)

gratuity is charged on final amount then is it not obvious to calculate such as!

just wish to have clarification on the two :
1.) 270 - 15% of 270 = 175.95/ 15 = 11.73

2.) if 115 is 270 then 100 = 180 and 180/15 = 12

is it not the same thing ?

Tip is charged on the bill. Consider this: the bill is $100 and tip is 15% means that total amount paid is 100+15=$115.

The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? A. 11.73 B. 12 C. 13.8 D. 14 E. 15.87 Bill*1.15=$207 --> Bill=$180 --> per person=$180/15=$12. Answer: B. _________________ Kudos [?]: 129372 [4], given: 12197 Manager Joined: 17 Sep 2011 Posts: 191 Kudos [?]: 139 [0], given: 8 The price of lunch for 15 people was$207 including a 15% [#permalink]

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10 May 2012, 03:22
The solution is :

207 * .15 = 31.05 ==> 207 - 31.05 = 175.95==> 175.95 / 15 = 11.73
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Re: The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 14 May 2012, 06:10 enigma123 wrote: The price of lunch for 15 people was$207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

A. 11.73
B. 12
C. 13.8
D. 14
E. 15.87

How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05 Price EXCLUDING gratuity = 207 - 31.05 = 175.95 Average price per person = 175.95/15 = 11.73 Hello here is my approach so let x be the sum of the 15 lunch WITHOUT the 15 % 1.15 X = 207 X = 207/ 1.15 X= 180 so 180 is for 15 people the average price be 180 /15= 12 HENCE B HOPE THIS HELP BEST REGARDS Kudos [?]: 37 [0], given: 12 Intern Joined: 19 Dec 2011 Posts: 19 Kudos [?]: 10 [1], given: 37 The price of lunch for 15 people was$207.00, including a [#permalink]

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25 Aug 2012, 12:33
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check the option :

12

12 * 15 = 180

180 + [ 18 + 9 ] ( 15 % of 180) = 207

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27 Feb 2013, 21:31
Can someone please explain how you compute 207/1.15 under two minutes quickly? I think my division need help
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07 May 2014, 15:06
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For those who are intimidated by the division I found back solving to be very efficient for this problem.

I started with D $14.00 14*15 = 210 210>207 and that doesn't even have the gratuity added. So I know right there that D and E are out and a 20 cent deduction on choice C is probably still going to be too high. Went to answer choice B.$12.00

12*15=180 15% of 180=27 180+72=207.00

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The price of lunch for 15 people was $207 including a 15% [#permalink] ### Show Tags 12 May 2014, 02:55 1 This post received KUDOS 1 This post was BOOKMARKED The price of lunch for 15 people was$207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

A. 11.73
B. 12
C. 13.8
D. 14
E. 15.87

here is my trouble:

the answer is B, because people say that the "15%" means 15% of the real amount, by say real amount, I mean the amounts these guys paid for what they ate.
but what puzzled me is that,
the subject of the sentence is "the price", which equals to $207, so, in my opinion, the following "15%" is to modify "the price", which is$207. if so, the gratuity must be $207*15%, and in this way, answer is A. so could anybody explain this to me? am i wrong? thanks a lot! Kudos [?]: 1 [1], given: 0 Math Expert Joined: 02 Sep 2009 Posts: 41912 Kudos [?]: 129372 [0], given: 12197 Re: The price of lunch for 15 people was$207 including a 15% [#permalink]

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12 May 2014, 03:00
MY42 wrote:
The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? A. 11.73 B. 12 C. 13.8 D. 14 E. 15.87 here is my trouble: the answer is B, because people say that the "15%" means 15% of the real amount, by say real amount, I mean the amounts these guys paid for what they ate. but what puzzled me is that, the subject of the sentence is "the price", which equals to$207, so, in my opinion, the following "15%" is to modify "the price", which is $207. if so, the gratuity must be$207*15%, and in this way, answer is A.

so could anybody explain this to me? am i wrong?
thanks a lot!

Merging similar topics. please refer to the discussion above.

Hope it helps.
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12 Sep 2014, 06:42
enigma123 wrote:
The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? (A)$11.73
(B) $12.00 (C)$13.80
(D) $14.00 (E)$15.87

[Reveal] Spoiler:
How come the answer is B?

This is how I solved it and got A, which is incorrect.

$207 includes 15% gratuity so 0.15 * 207 = 31.05 Price EXCLUDING gratuity = 207 - 31.05 = 175.95 Average price per person = 175.95/15 = 11.73 let x be the total without gratuity.. then we shall form x+0.15x = 207 1.15x=207 x=207/1.15 x=180. x/15 for each person then 180/15 = 12.. Kudos [?]: 31 [0], given: 81 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1853 Kudos [?]: 2632 [0], given: 193 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) The price of lunch for 15 people was$207.00, including a 15 [#permalink]

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31 Oct 2014, 00:34
Per head without gratuity $$= \frac{207 * 100}{115 * 15} = \frac{900}{75} = 12$$

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 07 Jan 2015, 13:19 The price included a gratuity of 15% on top of the original bill, hence$207.00 represents 115% of bill $x.yz$207.00 ------- 115%
$x.yz ---------- 100% x =$180.00

Bill per person: $180.00 : 15 =$12.00

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 03 May 2016, 11:38 1 This post received KUDOS Expert's post enigma123 wrote: The price of lunch for 15 people was$207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?

(A) $11.73 (B)$12.00
(C) $13.80 (D)$14.00
(E) $15.87 [Reveal] Spoiler: How come the answer is B? This is how I solved it and got A, which is incorrect.$207 includes 15% gratuity so 0.15 * 207 = 31.05

Price EXCLUDING gratuity = 207 - 31.05 = 175.95

Average price per person = 175.95/15 = 11.73

Solution:

An easy way to solve this problem is to translate what is provided in the question into a mathematical equation. We know that the total bill for 15 people was 207 dollars, including the 15 percent gratuity. We use the value 1.15 in the equation below to account for the meal itself plus the gratuity. We can use x as the average cost per person for the meal without the gratuity. Thus, we can say:

(1.15)(15)(x) = 207

(115/100)(15)(x) = 207

(115)(15)(x) = (207)(100)

We can divide the entire equation by 3. Doing so gives us:

(115)(5)(x) = (69)(100)

We can divide the entire equation by 5 and we get:

(115)x = (69)(20)

We can again divide the entire equation by 5 and we get:

(23)x = (69)(4)

We can again divide the entire equation by 23 and we get:

x = (3)(4)

x = 12

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Re: The price of lunch for 15 people was $207.00, including a 15 [#permalink] ### Show Tags 06 May 2016, 18:08 I had to think about this for a second, but here was my way of trudging through without much math (just at the end) x = tab without tip tip = 15% (total of 207 = 115%x) 207 = (115x/100) 207(100) = 115x 207(100) / 115 = x 207 = 3(3)23 100 = 2(2)(5)(5) 115 = 5(23) so..... (3*3*23)(2*2*5*5) / (5*23) = x cancel out like variables 3*3*2*2*5 = x 9*4*5 = 180 180 / 15 = 12.00 per person Kudos [?]: 6 [0], given: 0 Re: The price of lunch for 15 people was$207.00, including a 15   [#permalink] 06 May 2016, 18:08

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