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29 Aug 2025, 05:24
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John bought one book and paid the price marked inside the book plus sales tax with a $20 bill. He received exact change, which was less than $5. The sales tax was 9% of the book’s marked price. Which of the following must be true?
Indicate all that apply.
A. The marked price of the book was more than $13.50.
B. The marked price of the book was less than $18.50.
C. The sales tax on the book was less than $1.50.
Indicate all that apply.
A. The marked price of the book was more than $13.50.
B. The marked price of the book was less than $18.50.
C. The sales tax on the book was less than $1.50.
Updated on: 30 Aug 2025, 09:40
Originally posted by Sajjad1994 on 30 Aug 2025, 09:36.
Last edited by Sajjad1994 on 30 Aug 2025, 09:40, edited 1 time in total.
Last edited by Sajjad1994 on 30 Aug 2025, 09:40, edited 1 time in total.
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Official Explanation
Let b = the marked price of the book. The sales tax is 9% of the book’s marked price, so tax = .09 b. Then the cost of the book plus tax is given by \(1b + .09b,\) which equals 1.09b. Since John received change for his $20 bill, and since the change was less than $5, he must have spent between $15 and $20. Then \($15 < 1.09b < $20.\) Divide all three parts of this inequality by 1.09 to obtain $13.76 < b < $18.35. This result implies both (A) and (B), because b is certainly greater than $13.50 but less than $18.50. Choice (C) is not true, because if the marked price were $18, for example, then the sales tax would have been .09 × $18 = $1.62, which is greater than $1.50, while the total price remains low enough, $19.62, to leave John change, as required.
Answer: A,B
Let b = the marked price of the book. The sales tax is 9% of the book’s marked price, so tax = .09 b. Then the cost of the book plus tax is given by \(1b + .09b,\) which equals 1.09b. Since John received change for his $20 bill, and since the change was less than $5, he must have spent between $15 and $20. Then \($15 < 1.09b < $20.\) Divide all three parts of this inequality by 1.09 to obtain $13.76 < b < $18.35. This result implies both (A) and (B), because b is certainly greater than $13.50 but less than $18.50. Choice (C) is not true, because if the marked price were $18, for example, then the sales tax would have been .09 × $18 = $1.62, which is greater than $1.50, while the total price remains low enough, $19.62, to leave John change, as required.
Answer: A,B
