OG11-DS141

evey

On Jane's creditcardaccount, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane's creditcardaccount had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?

(1) Jane's payment was credited on the 21st day of the billing cycle.

(2) The average daily balance through the 25th day of the billing cycle was $540.

Ans
題目說總共欠了$600 還了$300 那麼列式應該為(600-300)除以30呀
為何OG解釋是 [x*600+(30-x)*300]/30  呢?

bigpig

注意，题目问的是what was the average daily balance on Jane's account for the billing cycle?

它问的是平均数，而根据前面题目对平均数的定义： the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days.

翻译成中文应为，一个30天账单周期的日平均余额 是 30天中所有天数的日余额的算术平均数（也就是说，30中，每一天的日余额相加之和再除以30天）

然后题目说，在30天的账单周期开始之时，Jane的信用卡账户有600美刀的余额，在30天的账单周期期间，她又付了300美刀进账户，所以从30天账单周期中的某一天起，她的余额就变成了600-300=300美刀了。根据“一个30天账单周期的日平均余额”的定义，在Jane支付那300美刀之前，每一天的日余额都为600美刀没有变化，所以是（600美刀/天 * X天），之后她向账户里付了300美刀之后，账户余额只剩下300美刀了，所以剩下的(30-x)天中每日的日余额都为300美刀，所以是（300美刀/天 * X天）。因此，答案是[x*600+(30-x)*300]/30。

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