GMAT
题目
A certain airline's fleet consisted of 60 Type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the Type A planes and acquired 4 new Type B planes. How many years did it take before the number of Type A planes left in the airline's fleet was less than 50 percent of the fleet?
解析
### 代数解法：
设\( x \)为A、B两种飞机达到收支平衡，且B型飞机数量刚好超过A型飞机所需的年数。
即：\( x \)年后，年增速为4的B型飞机数量，将刚好超过（现有60架A型飞机库存，按年减少3架的速率在\( x \)年后的剩余数量）。
列式：\( 4x ≥ 60 - 3x \)
化简得：\( 7x ≥ 60 \)
计算得：\( x ≥ 8.57 \)
向上取整为整数：\( x = 9 \)年
因此选项D是正确答案。
补充说明：这道题类似水箱问题——一个水管注水，另一个水管以不同速率排水。
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