PP PS 2 Q56

[nemolee]

To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

(A) X/T
(B)X/ (T-S)
(C) SX / (T-X)
(D) SX/ T(T-S)
(E) X(T-S) / T

ANS: D

我選到了 C ，讓我掉了一滴汗。。。
請問這題如何解？不了解為什麼(D)的答案中，分母還要多乘個 T ?
題目不是說在辦公司內一共有 T人嗎？這些 T 人本來要共同分擔餐費，後來有 S人不付錢了，所以應該就直接 T-S 就好了，所以我才會選到 C

請問為什麼選 (D) 謝謝..

[小花]

費用X ,T人分攤
每人分攤X/T元

費用X, (T-S)人分攤
每人分攤X/T-S元


X/(T-S)-X/T(通分)
=XT/T(T-S)-X(T-S)/T(T-S)
=XS/T(T-S)

[nemolee]

要通分 >< , 証明我是個急性子，每每遇到這種送人的餐會吃吃喝喝完之後就乖乖的當個分母付錢走人....
又忘了，這是數學題.... 可見，先前充當分母ㄉ我可能虧大了..
謝謝小花