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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 o
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 o
admin
2014-08-13
30
问题
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.
选项
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.
答案
C
解析
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
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(0.04)(9.61)≈0.38. 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.
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