If 50 people paid a total of $110 for tickets to attend a certain high school play and spent a total of $100 for refreshments at intermission, how many adults attended the play?(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets

题目

If 50 people paid a total of $110 for tickets to attend a certain high school play and spent a total of $100 for refreshments at intermission, how many adults attended the play?

(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.

(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.

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

观看戏剧的成人数量 = $ x $ 观看戏剧的儿童数量 = $ y $ 已知：如果有50人付费…… $ x + y = 50 $ ——（1） **陈述1** （1）每位观看戏剧的成人花3美元买票，每位观看戏剧的儿童花1美元买票。 $ 3x + y = 110 $ ——（2）用方程（2）减去方程（1）： $ 2x = 60 $ $ x = 30 $ 所以有30位成人观看了戏剧。该陈述足以回答目标问题。排除B、C、E。 **陈述2** （2）每位观看戏剧的成人在中场休息时花2美元买点心，每位儿童在中场休息时花2美元买点心。 $ 2x + 2y = 100 $ $ x + y = 50 $ 我们已经从题目题干中知道这个信息了。因此，该陈述没有提供额外信息。仅该陈述不足以求出观看戏剧的成人数量。排除D。 **选项A**

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