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A couple spent $264 in total while dining out and paid this amount usi

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A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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Tough and Tricky questions: Word Problems.



A couple spent $264 in total while dining out and paid this amount using a credit card. The $264 figure included a 20 percent tip which was paid on top of the price of the food which already included a sales tax of 10 percent. What was the actual price of the meal before tax and tip?

A) $184
B) $200
C) $204
D) $216
E) $232

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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 02 Dec 2014, 10:22
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The problem states that $264 includes the total price of food + tax, which an additional 20% tip. This means the $264 bill is 120% of the price of food + tax. So, the $264 = 1.2 (price of food + tax), the price of food + tax = $220.

This cost now includes the price of the food plus a 10% sales tax. So, the $220 is 110% of the price of the food. So, the price of only the food is $200.

Choice B--definitely had to read the wording a few times and I still feel confused
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 02 Dec 2014, 20:03
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Answer = B) $200

Bill (Meal + Tax + Tip) = 264

Bill (Meal + Tax) \(= 264 * \frac{100}{120} = 220\)

Bill only Meal \(= 220 * \frac{100}{110} = 200\)
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 02 Dec 2014, 20:34
If x is actual price then,
(x * 1.1)*1.2 = 264
(x * 1.1)*1.2 = 24 * 11
x = 20*10 = 200
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 02 Dec 2014, 21:48
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Let x be the actual price of the meal before tax and tip
264 = 120% of ( x + 10% tax)
= 120% of (1.1x)
= 1.2(1.1x)
= 1.32x

x = 264/1.32 = 26400/132 = 200


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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 15 Jun 2016, 13:40
consider price of the meal as x dollars
after a 10% sales tax addition price becomes 1.1*x
finally after a 20% tip on this amount it becomes 1.2*1.1*x = 1.32x
but this amount is given as $264
1.32x = 264
x = 200
Correct Answer - B
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 22 Oct 2016, 17:40
This can be solved using the following formula:

1.1x+0.20(1.1x) = 264

You'll find x = 200
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 23 Oct 2016, 02:10
Bunuel wrote:
A couple spent $264 in total while dining out and paid this amount using a credit card. The $264 figure included a 20 percent tip which was paid on top of the price of the food which already included a sales tax of 10 percent. What was the actual price of the meal before tax and tip?

A) $184
B) $200
C) $204
D) $216
E) $232


Food Bill = 100 (Say)
Sales Tax = 10
Food Bill + Tax = 110
Tip = 22
Food Bill + Tax + Tip = 132

So, When (Food Bill + Tax + Tip) is 132 , food bill is 100

Or, When (Food Bill + Tax + Tip) is 264 , food bill is \(\frac{100}{132}*264\) = 200

Hence answer will be (B)
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Re: A couple spent $264 in total while dining out and paid this amount usi [#permalink]

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New post 25 Dec 2017, 19:56
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Re: A couple spent $264 in total while dining out and paid this amount usi   [#permalink] 25 Dec 2017, 19:56
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