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At a certain restaurant, the price of a sandwich is $ 4.00 more than

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Bunuel
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At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   03 Jan 2016, 12:28
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At a certain restaurant, the price of a sandwich is $ 4.00 more than the price of a cup of coffee. If the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, what is the price of a cup of coffee, EXCLUDING the sales tax?

A. $ 1.50
B. $ 3.00
C. $ 4.00
D. $ 5.50
E. $ 7.00
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   06 Jan 2016, 12:00
Let the price of sandwhich = S
price of coffee = C
S= C+4
=> S - C = 4 --1
the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%,
1.05(S+C) = 7.35
=> S+C = 7 --2

From equations 1 and 2, we get
S=5.5$
C= 1.5$

Answer A
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   17 Feb 2017, 09:35
Bunuel wrote:
At a certain restaurant, the price of a sandwich is $ 4.00 more than the price of a cup of coffee. If the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, what is the price of a cup of coffee, EXCLUDING the sales tax?

A. $ 1.50
B. $ 3.00
C. $ 4.00
D. $ 5.50
E. $ 7.00


On scanning the options, only option A will give a total amount less than 7.35$.i.e 1.5+5.5=7. Rest of the options will give an amount greater than 7.35$ and that's impossible given the total cost of sandwich and coffee inclusive of tax is 7.35$.

Hence A.
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   23 Feb 2017, 10:28
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Bunuel wrote:
At a certain restaurant, the price of a sandwich is $ 4.00 more than the price of a cup of coffee. If the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, what is the price of a cup of coffee, EXCLUDING the sales tax?

A. $ 1.50
B. $ 3.00
C. $ 4.00
D. $ 5.50
E. $ 7.00


We can let c = the price of a cup of coffee and s = the price of a sandwich and create the following equation:

s = 4 + c

We are also given that the price of a sandwich and cup of coffee is $7.35, including a 5% sales tax. Thus:

1.05(c + s) = 7.35

c + s = 7.35/1.05 = 7

Thus, excluding the 5% sales tax, c + s = 7.

Finally, we can substitute 4 + c for s in the equation c + s = 7 and we have:

c + 4 + c = 7

2c = 3

c = $1.50

Answer: A
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   23 Feb 2017, 10:39
Bunuel wrote:
At a certain restaurant, the price of a sandwich is $ 4.00 more than the price of a cup of coffee. If the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, what is the price of a cup of coffee, EXCLUDING the sales tax?

A. $ 1.50
B. $ 3.00
C. $ 4.00
D. $ 5.50
E. $ 7.00


\(s + c = 7.00\) ( Ex S.tax )

Now, \(s = c + 4\)

Or, \(( c + 4 ) + c = 7\)

Or, \(2c = 3\)

Or, \(c = 1.5\)

Thus, price of a cup of coffee, EXCLUDING the sales tax is $ 1.50 , answer will be (A) $ 1.50
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink] New post   07 May 2022, 02:53
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Re: At a certain restaurant, the price of a sandwich is $ 4.00 more than [#permalink]
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