牧場共有500隻羊和豬，賣掉四分之一的豬，再買回60隻羊後，羊和豬的數量相同。原有_______隻羊和_______隻豬。
請列式說明，謝謝。
小六數學思考題
2007-01-06 7:32 am
回答 (7)
2007-01-06 7:39 am
✔ 最佳答案
X= 豬Y=羊
X+Y=500
3/4 (X)=Y+60
SO. 豬有320隻, 羊有180隻
2007-01-06 5:40 pm
180隻豬和320隻羊
2007-01-06 7:54 am
設牧場有豬 m 隻 , 羊有 ( 500 - m ) 隻
m x ( 1 - 1/4 ) = ( 500 - m ) + 60
3/4 m = 500 - m + 60
m + 3/4 m = 500 + 60
1 /3 /4 m = 560
m = 560 ÷ 1 /3 /4
m = 560 x 4 / 7
m = 320
∴ 原有羊 ( 500 - 320 ) = 180 隻 , 豬 = 320 隻
2007-01-06 7:53 am
設豬的數量為a , 羊的數量為b
a+b=500 --(1)
3/4 a=60+b --(2)
a=500-b --(3)
把(3)代進(2):3/4(500-b)=60+b
375-0.75b=60+b
375-60=b+0.75b
315=1.75b
b=180
再代b=180入(1):a+180=500
a=320
所以，有320隻豬和180隻羊。
a+b=500 --(1)
3/4 a=60+b --(2)
a=500-b --(3)
把(3)代進(2):3/4(500-b)=60+b
375-0.75b=60+b
375-60=b+0.75b
315=1.75b
b=180
再代b=180入(1):a+180=500
a=320
所以，有320隻豬和180隻羊。
參考: 自己
2007-01-06 7:51 am
Let x be the no. of pig and y be the no. of sheep.
x+y=500.........(1)
x(3/4)=y+60........(2)
From (1),
x=500-y.........(3)
From (2),
3x/4=y+60
3(500-y)=4y+240
1500-3y=4y+240
7y=1260
y=180
From (3),
x=500-(180)
x=320
so
牧場共有320隻豬和180隻羊
x+y=500.........(1)
x(3/4)=y+60........(2)
From (1),
x=500-y.........(3)
From (2),
3x/4=y+60
3(500-y)=4y+240
1500-3y=4y+240
7y=1260
y=180
From (3),
x=500-(180)
x=320
so
牧場共有320隻豬和180隻羊
2007-01-06 7:49 am
設羊和豬分別有x和y隻
x+y=500..[1]
(1-1/4)x=y+60..[2]
form[1]
x+y=500
x=500-y..[3]
put [3] into [2]
(1-1/4)x=y+60
3/4(500-y)=y+60
375-3/4y=y+60
315=7/4y
y=180..[4]
put [4] into [3]
x=500-180
x=320
so,原有羊320隻和豬180隻
2007-01-05 23:52:11 補充：
sori..調轉左=口='''設豬和羊分別有x和y隻x y=500..[1](1-1/4)x=y 60..[2]form[1]x y=500x=500-y..[3]put [3] into [2](1-1/4)x=y 603/4(500-y)=y 60375-3/4y=y 60315=7/4yy=180..[4]put [4] into [3]x=500-180x=320so,原有豬320隻和羊180隻
x+y=500..[1]
(1-1/4)x=y+60..[2]
form[1]
x+y=500
x=500-y..[3]
put [3] into [2]
(1-1/4)x=y+60
3/4(500-y)=y+60
375-3/4y=y+60
315=7/4y
y=180..[4]
put [4] into [3]
x=500-180
x=320
so,原有羊320隻和豬180隻
2007-01-05 23:52:11 補充：
sori..調轉左=口='''設豬和羊分別有x和y隻x y=500..[1](1-1/4)x=y 60..[2]form[1]x y=500x=500-y..[3]put [3] into [2](1-1/4)x=y 603/4(500-y)=y 60375-3/4y=y 60315=7/4yy=180..[4]put [4] into [3]x=500-180x=320so,原有豬320隻和羊180隻
參考: me
2007-01-06 7:44 am
x=豬
y=羊
1: 500=x+y
2: 3x/4=y+60
將1.轉成: x=500-y
將改了的1.代入2.即: 3(500-y)/4=y+60
1500-3y=(y+60)*4
1500-3y=4y+240
7y=1260
y=180
將答案放回1.: x=500-180
x=320
答案: 180隻豬和320隻羊
y=羊
1: 500=x+y
2: 3x/4=y+60
將1.轉成: x=500-y
將改了的1.代入2.即: 3(500-y)/4=y+60
1500-3y=(y+60)*4
1500-3y=4y+240
7y=1260
y=180
將答案放回1.: x=500-180
x=320
答案: 180隻豬和320隻羊
收錄日期: 2021-04-12 22:01:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070105000051KK04686