小明第一次用３６元買了若干合牛奶，第二次買的時候呢個牌子減价，每合便宜０．３元，小明同樣用３６元買這種牛奶，比第一次多買了４合，問小明第一次買了多少合牛奶？
請幫忙解答，請詳細解析。
呢條題應該點解？
2008-01-02 11:24 pm
回答 (2)
2008-01-02 11:37 pm
✔ 最佳答案
設$x為原價,y為第一次用３６元可買的牛奶數目xy = 36--------------------------------(1)
(x-0.3)(y+4) = 36-------------------(2)
由(1),x = 36/y------------------------(3)
將(3)代入(2)
(36/y - 0.3)(y + 4) = 36
(36 - 0.3y)(y + 4) = 36y
36y - 0.3y^2 + 144 - 1.2y = 36y
0.3y^2 + 1.2y - 144 = 0
y = 20 或 y = -24(捨去)
∴小明第一次買了20合牛奶
參考: 其實應該是「盒」而不是"合",敬請留意
2008-01-03 4:35 am
Let x be the original price,and y be the no. of milk at the first time.
then we have,
xy=36
x=36/y............(1)
(x-0.3)(y+4)=36
xy+4x-0.3y-1.2=36
xy+4x-0.3y=37.2......(2)
sub (1) into (2)
y(36/y)+4(36/y)-0.3y=37.2
36+144/y-0.3y=37.2
144/y-0.3y=1.2
144-0.3y^2=1.2y
0.3y^2+1.2y-144=0
y^2+4y-480=0
(y+24)(y-20)=0
y=20 or-24(reject)
therefore he buy 20 box at the first time.
then we have,
xy=36
x=36/y............(1)
(x-0.3)(y+4)=36
xy+4x-0.3y-1.2=36
xy+4x-0.3y=37.2......(2)
sub (1) into (2)
y(36/y)+4(36/y)-0.3y=37.2
36+144/y-0.3y=37.2
144/y-0.3y=1.2
144-0.3y^2=1.2y
0.3y^2+1.2y-144=0
y^2+4y-480=0
(y+24)(y-20)=0
y=20 or-24(reject)
therefore he buy 20 box at the first time.
收錄日期: 2021-04-13 14:52:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080102000051KK01815