2019 AMC 8 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.

Gilda 有一袋弹珠。她把其中 20%20\% 给了朋友 Pedro。然后她把剩下弹珠的 10%10\% 给了另一位朋友 Ebony。最后,她把袋中此时剩下弹珠的 25%25\% 给了弟弟 Jimmy。Gilda 自己还剩原来那袋弹珠的百分之多少?

Gilda has a bag of marbles. She gives 20%20\% of them to her friend Pedro. Then Gilda gives 10%10\% of what is left to another friend, Ebony. Finally, Gilda gives 25%25\% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?

2020

331333\dfrac{1}{3}

3838

4545

5454

答案:E
知识点:百分数
难度评级:960
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文字解答:

假设 Gilda 原来有 100100 颗弹珠。给 Pedro 2020 颗后,还剩 10020=80100 - 20 = 80 颗。

接着她给 Ebony 80×.1=880 \times .1 = 8 颗,还剩 808=7280 - 8 = 72 颗。

最后她给 Jimmy 72×.25=1872 \times .25 = 18 颗,还剩 7218=5472 - 18 = 54 颗,也就是原来的 54%54\%

正确答案是 E

Assume that Gilda starts off with 100100 marbles. After giving 2020 marbles to Pedro, she has 10020=80100 - 20 = 80 marbles left.

She then gives 80×.1=880 \times .1 = 8 marbles to Ebony, with her having 808=7280 - 8 = 72 marbles left.

Finally, Gilda gives 72×.25=1872 \times .25 = 18 marbles to Jimmy. She has a total of 7218=5472 - 18 = 54 marbles left, which is 54%54\% of her original total.

Thus, the correct answer is E.

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