2015 AMC 10B 第 4 题

Question

四个兄弟姐妹点了一张特大披萨。Alex 吃了披萨的

\frac15

，Beth 吃了

\frac13

，Cyril 吃了

\frac14

。Dan 吃了剩下的部分。按吃掉披萨的份额从大到小排列，顺序是什么？

Four siblings ordered an extra large pizza. Alex ate

\frac15,

Beth

\frac13,

and Cyril

\frac14

of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of the pizza they consumed?

Alex, Beth, Cyril, Dan

Beth, Cyril, Alex, Dan

Beth, Cyril, Dan, Alex

Beth, Dan, Cyril, Alex

Dan, Beth, Cyril, Alex

知识点：分数

Dan 得到

1-\frac15-\frac13-\frac14

。

Dan receives

1-\frac15-\frac13-\frac14

把所有份额都化为分母

60

的分数来比较。

Compare all shares with denominator

60

因为

\frac 13 > \frac 14 > \frac 15

，所以 Beth 吃得比 Cyril 多，Cyril 吃得比 Alex 多。因此这三人的顺序已经确定。

Dan 吃了

1- \dfrac 13 - \dfrac 14 - \dfrac 15 = \dfrac{13}{60}\text{。}

这大于

\frac 15

，小于

\frac 14

，所以 Dan 排在 Cyril 和 Alex 之间，顺序为 Beth、Cyril、Dan、Alex。

所以正确答案是 C。

Since

\frac 13 > \frac 14 > \frac 15,

we know Beth ate more than Cyril and Cyril ate more than Alex. Thus, those three are in order.

The amount Dan ate is

1- \dfrac 13 - \dfrac 14 - \dfrac 15 = \dfrac{13}{60}.

This is greater than

\frac 15

and less than

\frac 14 ,

so Dan is in between Cyril and Alex. This makes the order Beth, Cyril, Dan, Alex.

Thus, the correct answer is C .

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