2009 AMC 10A 第 8 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

8.

Wen 家三代人去看电影,每一代有两人。最年轻一代的两人作为儿童享受 50%50\% 折扣。最年长一代的两人作为老人享受 25%25\% 折扣。中间一代的两人没有折扣。Wen 祖父的一张老人票价为 $6.00\$6.00,他要为所有人付钱。他一共要付多少美元?

Three generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a 50%50\% discount as children. The two members of the oldest generation receive a 25%25\% discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs $6.00,\$6.00, is paying for everyone. How many dollars must he pay?

3434

3636

4242

4646

4848

答案:B
知识点:百分数逆推法
难度评级:1060
解答:

老人票价为 $6\$6,这是全价的 34\dfrac34,所以全价票为 436=$8\dfrac43 \cdot 6 = \$8,儿童票为 128=$4\dfrac12 \cdot 8 = \$4

总价为 2(6+8+4)=$36.2(6 + 8 + 4) = \$36.

所以正确答案是 B

The senior ticket costs $6,\$6, which is 34\dfrac34 of the full price, so a full ticket costs 436=$8,\dfrac43 \cdot 6 = \$8, and a child ticket costs 128=$4.\dfrac12 \cdot 8 = \$4.

The total is 2(6+8+4)=$36.2(6 + 8 + 4) = \$36.

Thus, the correct answer is B.

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