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20 Jun 2024, 13:49
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
16% (01:27) correct
83% (03:07) wrong based on 6 sessions
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The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true?
Indicate all such statements.
A. The price of the book was less than $9.50.
B. The price of the book was greater than $6.90.
C. The sales tax was less than $0.45
Indicate all such statements.
A. The price of the book was less than $9.50.
B. The price of the book was greater than $6.90.
C. The sales tax was less than $0.45
26 Jun 2024, 12:45
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Official Explanation
For this problem you may find it helpful to translate the given information into an algebraic expression. Since the price of the book is unknown, you can call it x dollars, and then the total amount that Mary paid is x dollars plus 4% of x dollars, or 1.04x dollars. The problem states that Mary received some change from a $10 bill, so 1.04x dollars must be less than $10. Since the change was less than $3.00, the total amount Mary paid for the book must have been greater than $7.00. You can express this information algebraically by the inequality
Solving the inequality for x by dividing by 1.04, and rounding, you get
So you see that x, the price of the book, must be between $6.73 and $9.62, and each price in between is possible. With this information, you can quickly examine the first two statements. Choice A is not necessarily true because the price could be as high as $9.61, and Choice B is not necessarily true because the price could be as low as $6.74.
To examine Choice C, you could compute the tax for the greatest possible price, which would be 4% of 9.61, or . Since this greatest possible tax is less than $0.45, Choice C must be true. You can also quickly see that Choice C must be true if you note that 4% of $10.00 would only be $0.40, and since the price must be less than $10.00, the tax must be less than $0.40.
The correct answer consists of Choice C.
For this problem you may find it helpful to translate the given information into an algebraic expression. Since the price of the book is unknown, you can call it x dollars, and then the total amount that Mary paid is x dollars plus 4% of x dollars, or 1.04x dollars. The problem states that Mary received some change from a $10 bill, so 1.04x dollars must be less than $10. Since the change was less than $3.00, the total amount Mary paid for the book must have been greater than $7.00. You can express this information algebraically by the inequality
\(7.00<1.04x<10.00\)
Solving the inequality for x by dividing by 1.04, and rounding, you get
\(6.73<x<9.62\)
So you see that x, the price of the book, must be between $6.73 and $9.62, and each price in between is possible. With this information, you can quickly examine the first two statements. Choice A is not necessarily true because the price could be as high as $9.61, and Choice B is not necessarily true because the price could be as low as $6.74.
To examine Choice C, you could compute the tax for the greatest possible price, which would be 4% of 9.61, or . Since this greatest possible tax is less than $0.45, Choice C must be true. You can also quickly see that Choice C must be true if you note that 4% of $10.00 would only be $0.40, and since the price must be less than $10.00, the tax must be less than $0.40.
The correct answer consists of Choice C.
