题目信息
There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?
A:45,000
B:360,000
C:364,500
D:392,000
E:396,900
参考答案及共享解析
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已选答案：
正确答案：
C:364,500
Algebra First-degree equations
Let h be the number of hardback copies of the novel that were sold after the paperback version was issued. The following table summarizes the given information.
Then, 441,000 = 36,000 + 10h or h = 40,500 and 9h = (9)(40,500) = 364,500.
The correct answer is C.
Alternate Solution
Arithmetic Ratios
From the moment the paperback version was issued, 441,000 – 36,000 = 405,000 copies of the novel were sold. Test the answer choices to see whether the ratio of paperbacks sold to hardbacks sold is 9:1. Start with the middle value, because the answer choices are usually listed in numerical order. This way, if you pick an answer that does not give the 9:1 ratio, you can learn whether it was too high or too low, thus allowing you to eliminate other answers that are too high or too low.
Testing answer choice C, if 364,500 paperbacks were sold, then 405,000 – 364,500 = 40,500 hardbacks were sold after the initial 36,000 hardbacks were sold. Noting that 40,500 hardbacks is 10% of 405,000 and 364,500 paperbacks is 90% of 405,000, the ratio of paperbacks to hardbacks is 9:1.
The correct answer is C.
Let h be the number of hardback copies of the novel that were sold after the paperback version was issued. The following table summarizes the given information.
| Hardbacks sold | Paperbacks sold | Total | |
| Before paperbacks | 36,000 | 0 | 36,000 |
| After paperbacks | h | 9h | 10h |
Then, 441,000 = 36,000 + 10h or h = 40,500 and 9h = (9)(40,500) = 364,500.
The correct answer is C.
Alternate Solution
Arithmetic Ratios
From the moment the paperback version was issued, 441,000 – 36,000 = 405,000 copies of the novel were sold. Test the answer choices to see whether the ratio of paperbacks sold to hardbacks sold is 9:1. Start with the middle value, because the answer choices are usually listed in numerical order. This way, if you pick an answer that does not give the 9:1 ratio, you can learn whether it was too high or too low, thus allowing you to eliminate other answers that are too high or too low.
Testing answer choice C, if 364,500 paperbacks were sold, then 405,000 – 364,500 = 40,500 hardbacks were sold after the initial 36,000 hardbacks were sold. Noting that 40,500 hardbacks is 10% of 405,000 and 364,500 paperbacks is 90% of 405,000, the ratio of paperbacks to hardbacks is 9:1.
The correct answer is C.
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