In this GRE math problem, we are given the information that Mary paid for a book with a $10 bill, which was equal to the price of the book plus a 4 percent sales tax. We are also told that she received the correct change, which was less than $3.
To solve this problem, we need to determine the range of possible prices for the book and the sales tax. Let's denote the price of the book as x and the sales tax as 0.04x.
From the given information, we have the equation:
x + 0.04x = 10
1.04x = 10
x = 10 / 1.04
x ≈ $9.6154
Therefore, the price of the book is approximately $9.62.
Now, let's check the statements to see which ones must be true.
A. The price of the book was less than $9.50.
Since the price of the book is $9.62, this statement is false.
B. The price of the book was greater than $6.90.
Since the price of the book is $9.62, this statement is true.
C. The sales tax was less than $0.45.
The sales tax is 4 percent of the price of the book, which is 0.04 * $9.62 = $0.3848. Therefore, this statement is true.
In summary, the correct statements are:
- The price of the book was greater than $6.90
- The sales tax was less than $0.45
Therefore, the solution to this GRE math problem is that the price of the book was $9.62 and the sales tax was $0.3848. Mary received the correct change, which was less than $3.00.
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