a, b, and c

問:
Given that 2a/25 = 3b/38 = 4c/49 , where a, b, and c are positive. Arrange a, b, and c in ascending order.

解:
Note that the fractions are all equal, say, to some positive R.
Then, we get a = (25/2)R = (12 + 1/2)R .
Likewise, b = (12 + 2/3)R , and c = (12 + 1/4)R .
Hence, c < a < b .

(或者快一點:
...Then, we get
a = (12 + 1/2)R , b = (12 + 2/3)R , and c = (12 + 1/4)R ,
which obviously reveals c < a < b .)



這個題解的風格, 跟一般中學教科書不同. 我想題解不宜過於詳細, 連做簡化的步驟也羅列無遺. 步驟太拖沓, 關鍵都湮沒於枝節之中, 反而難以掌握. 好的題解, 也是高明的講解, 只有恰當地跳步, 才能幫助同學觸類旁通.



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PS: 最簡單的答法, 莫過於乞靈於計算機

Roughly, 0.08a = 0.079b = 0.082c .
Hence, c is the smallest, and b is the largest.