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...

swerve wrote: ↑

Wed Mar 11, 2020 9:53 am

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

The OA is A

Source: Princeton Review

Given that the price of a sandwich and a cup of coffee is $ 7.35, including a sales tax of 5%, the price of a sandwich and a cup of coffee is $ 7.35, excluding a sales tax = 7.35/1.05 = $7.00

Say the price a cup of coffee = x; thus, the price of a sandwich = $4 + x

=> x + 4 + x = 7 => x = $1.50.

The correct answer: A

Hope this helps!

-Jay
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swerve wrote: ↑

Wed Mar 11, 2020 9:53 am

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

The OA is A

Source: Princeton Review

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