A store purchased coats from a manufacturer at $40 each and then sold all of the coats

题目

A store purchased coats from a manufacturer at $40 each and then sold all of the coats. The store's gross profit on the sale of the coats was what percent of the store's revenue from the sale of the coats?

(1) The store sold 20 percent of the coats at $80 each and the rest of the coats at $60 each.

(2) The store's total revenue from the sale of the coats was $6,400.

选项

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

解析

设此次交易中外套的数量为 $x$。因此，成本价（C.P.）= $40x$，售价（S.P.）= $a \times x$（其中 $a$ 为单件外套的售价）。我们需要满足：$\left(\frac{ax - 40x}{ax}\right) \times 100 = \left(1 - \frac{40x}{ax}\right) \times 100 \dots (i)$ $ax$ = 销售总营收。 (1) 商店以每件80美元的价格售出20%的外套，剩余外套以每件60美元的价格售出。 $ax = 0.2x \times 80 + 0.8x \times 60 \dots (ii)$ 将 $ax$ 的值代入公式 (i) 中，可计算出最终结果：公式分子与分母中的 $x$ 会相互抵消。 **充分（SUFF.）** (2) 商店销售外套的总营收为6400美元。根据此条件，代表外套数量的分子中的 $x$ 无法被消去。 **不充分（INSUFF.）** **答案：A**

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