请教一道小五名校试题的解法

saysorry

各位版友： 孩子在做买的小五的名校试卷。在南华小学的试卷中，有这样一道题：

A total of 360 teachers and pupils participated in tree planting. Each teacher planted 3 trees and each group of 3 pupils planted 2 trees. If 520 trees were planted, how many pupils were there?

答案是240没有问题。可是参考答案给出的解题过程用的是猜测的方法，我觉得非常不严谨；可我自己只能用方程来解这道题。
现想请教各位，能否用画model（不知道是不是这么拼，就是画图）的方法解出这道题？提前感谢各位。

lianlian.z

Assume all are teachers.
the total number of trees of planted should be: 360x3=1080 tress
actual number of trees: 520 trees
number of trees should be cut down by: 1080-520=560
every 3 teachers will plant 3x3=9 trees
every 3 pupils will plant 2 trees
change 3 teachers to 3 pupils, number of trees will decrease by : 9-2=7 trees
number of changes needed: 560 / 7 = 80 times
total number teachers changed to pupils is : 80x3=240 pupils

希望解释的清楚 ＝）

lianlian.z

Assume all are teachers.
the total number of trees of planted should be: 360x3=1080 tress
actual number of trees: 520 trees
number of trees should be cut down by: 1080-520=560
every 3 teachers will plant 3x3=9 trees
every 3 pupils will plant 2 trees
change 3 teachers to 3 pupils, number of trees will decrease by : 9-2=7 trees
number of changes needed: 560 / 7 = 80 times
total number teachers changed to pupils is : 80x3=240 pupils

frekiwang

each teacher plant 3 trees, each pupil plants 2/3 trees.

Teachers: 000000000  000000000  000000000  000000000  000000000  000000000 000000000...
Pupils:      00              00              00               00              00              00             00             ...
Each unit 0 = 1/3 tree

By adding a 0000000(7'0's to each pupil, each of them can plant as many trees as teachers. in total they will plant 9 x 360 = 3240 units. The fact is, there is a total of 520 x 3 = 1560 units.
=1680 units, this diffence is due to adding 7 units to each pupil.
1680 / 7 = 240, there are 240 pupils

davidbin

A total of 120 groups of teachers and pupils participated in tree planting. Every group has 3 persons. Each group of teachers planted 9 trees and each group of  pupils planted 2 trees. If 520 trees were planted, how many pupils were there? 这就变成了小三或小四题了(鸡兔同笼）
120 x9 -520 = 560
540 / (9-2) = 80 group of students
80X3 = 240

lianlian.z

@jjrchome  ： 谢谢您～ ^_^

saysorry

非常感谢上面各位热心老师的解答。可是女儿天资一般，尤其不擅长数学。她刚才看了几种解法，每种解法都说有不懂的地方。我还要硬着头皮消化了之后再讲给女儿听。其实这种题目如果用方程来解答一目了然，不用方程绕的弯太多了。但是自己多年不用数学，又不知如何教起。真是着急啊

bluesmama

saysorry 发表于 18-2-2013 21:18
非常感谢上面各位热心老师的解答。可是女儿天资一般，尤其不擅长数学。她刚才看了几种解法，每种解法都说有 ...

我也有同感！
我的也是小五，考卷还没开始做呢！眼看考试要到了！

毛絮

小五不学方程么?

lianlian.z

毛絮 发表于 18-2-2013 22:20
小五不学方程么?

小六开始学 而且也不鼓励用 :)