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求解曼哈顿一数学题(有答案,请着重看下红色字体部分)

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发表于 2011-8-12 15:02:19 | 只看该作者 回帖奖励 |倒序浏览 |阅读模式
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

12 greater

17 fewer

28 fewer

36 fewer

44 fewer








答案:
We know that the student to teacher ratio at the school is 16 to 1, and the total number of people is 510.  Therefore:
Number of students = (16/17)(510) = 480
Number of teachers = (1/17)(510) = 30

Kindergarten students make up 1/5 of the student population, so:
Number of kindergarten students = (1/5)(480) = 96

Fifth and sixth graders account for 1/3 of the remainder (after kindergarten students are subtracted from the total), therefore:
Number of 5th and 6th grade students = (1/3)(480 – 96) = (1/3)(384) = 128

Students in first and second grades account for 1/4 of all the students, so:
Number of 1st and 2nd grade students = (1/4)(480) = 120

So far, we have accounted for every grade but the 3rd and 4th grades, so they must consist of the students left over:
Number of 3rd and 4th grade students = Total students – students in other grades
Number of 3rd and 4th grade students = 480 – 96 – 128 – 120 =136
(此处不明白,为什么还要额外再减去96呢?文中不是说幼儿园学生也是5.6 grader吗?请看文中红色部分,是否我看错了?555~~我用7分钟做这题,结果还做错了。)

If there are an equal number of students in the third and fourth grades, then:
Number of 3rd grade students = 136/2 = 68

The number of students in third grade is 68, which is fewer than 96, the number of students in kindergarten. The number of students in 3rd grade is thus 96 – 68 = 28 fewer than the number of kindergarten students.

The correct answer is C.


谢谢大家!
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沙发
发表于 2011-8-12 15:14:49 | 只看该作者
红字的意思是学生包括从幼儿园到六年级的所有学生。
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