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# Twenty people had dinner together at a restaurant. The cost of the mea

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Math Expert
Joined: 02 Sep 2009
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Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

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01 Apr 2018, 10:34
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Difficulty:

35% (medium)

Question Stats:

70% (02:23) correct 30% (02:31) wrong based on 76 sessions

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Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

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Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

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01 Apr 2018, 11:07
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

Given:
20 people,
Total cost + 18 % Gratuity = 531

Need to find per person cost excluding the gratuity...
Method 1: Normal Calculations

average total cost will be less than average of total Cost + 18% Gratuity
=> average of total cost + Gratuity = 531/20
=> $$total cost < 531/20$$
=> total cost < 26.55
eliminate option C, D and E

Gratuity is little less than 20%
so for ease of calculation lets take gratuity as 20%

=> Average Total cost * 1.20 (20% gratuity) = Average (total cost + Gratuity)
=> $$Average total cost = 26.55/1.20$$
Approx = 22
as we increased the denominator from 1.18 to 1.2 the answer should be greater than 22 hence Option B

Method 2: Use the options

Pick the mid value -> 26.55
if that is the average cost than overall cost = 26.55 * 20 = 513.00,
Now 18% gratuity will result in an amount that is more than 531 hence all options equal to or greater than 26.55 are disqualified

move on to the next number 22.50
22.50 * 20 = 450
increase by 18% = 450 *1.18 = 531
this is what we were looking for hence answer is B

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Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

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01 Apr 2018, 15:59
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

D) $30.50 each? Round to$30
Total before gratuity is already too great.
$$\frac{30}{person}* 20(persons) = 600$$ - REJECT

Per person cost must be lower. Answers A, B, and C remain. Choose the round number, B.

Either B is too low and the answer is C; B is too high and the answer is A; or B is the answer.

B) $22.50 each? $$22.50 = 22\frac{1}{2}=\frac{45}{2}$$ Total before gratuity: $$\frac{45}{2}*20=450$$ Total with gratuity? Find 18% of$450, add it to $450 $$(\frac{18}{100}*450)=(\frac{9}{50}*450)=81$$ $$(81 + 450) = 531$$ MATCH Answer B Algebra Let $$x$$ = total cost of dinner without gratuity$531 includes a tip of 18% on original total, $$x$$

$$531 = 1.18x$$
$$x = \frac{531}{1.18}$$

$$1.18=1\frac{18}{100}=1\frac{9}{50}=\frac{59}{50}$$

$$x =\frac{531}{(\frac{59}{50})}=531*\frac{50}{59}$$

$$x=(531*\frac{50}{59})=(9*50)=450$$

Per person cost? $$(\frac{450}{20})=(\frac{45}{2})=22.50$$

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Re: Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

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01 Apr 2018, 22:32
1
Bunuel wrote:
Twenty people had dinner together at a restaurant. The cost of the meal plus an automatic gratuity of 18% for a large party was $531.00, before sales tax was added. What was the average price of the meal per person NOT INCLUDING the gratuity or sales tax? (A)$21.77
(B) $22.50 (C)$26.55
(D) $30.50 (E)$36.55

Cost + Gratuity @18% = 531

i.e. C+ (18/100)*C = 531

i.e. 1.18 C = 531

i.e. C = 531/1.18 = 450

The cost is shared by 20 people hence Cost per person = C/20 = 450/20 = 22.5

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Re: Twenty people had dinner together at a restaurant. The cost of the mea  [#permalink]

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26 Dec 2018, 12:35
Is there no shortcut for this question, instead of dividing 531 by 1.18?
Re: Twenty people had dinner together at a restaurant. The cost of the mea   [#permalink] 26 Dec 2018, 12:35
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