想問：
1)
兩個數之差為10，若較小的數4倍與較大的數的1/3之和是25，求該兩個數。
2)
老師把x張貼紙平均分給8位小朋友，每位小朋友分得5張貼紙，餘下3張，求貼紙的總數。
數學題..
2006-10-18 6:13 am
回答 (5)
2006-10-18 6:23 pm
=43
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2006-10-18 7:07 am
1)
Let x, y be the two no.
x+y=10...(i)
4y+1/3x=25...(ii)
from (i), x=10-y...(iii)
sub (iii) into (ii),
4y+1/3(10-y)=25
4y(3)+(10-y)=25(3)
12y+10-y=75
y=65/11
Sub y=65/11 into (i)
x+65/11=10
x=45/11
2)
x=8*5+3
x=43
2006-10-17 23:10:51 補充：
SOR,,睇錯,,上面既第一條is wrongx-y=10...(i)4y 1/3x=25...(ii)from (i), x=10 y...(iii)sub (iii) into (ii), 4y 1/3(10 y)=254y(3) (10 y)=25(3)12y 10 y=75y=5sub y=5 into (i)x-5=10x=15
Let x, y be the two no.
x+y=10...(i)
4y+1/3x=25...(ii)
from (i), x=10-y...(iii)
sub (iii) into (ii),
4y+1/3(10-y)=25
4y(3)+(10-y)=25(3)
12y+10-y=75
y=65/11
Sub y=65/11 into (i)
x+65/11=10
x=45/11
2)
x=8*5+3
x=43
2006-10-17 23:10:51 補充：
SOR,,睇錯,,上面既第一條is wrongx-y=10...(i)4y 1/3x=25...(ii)from (i), x=10 y...(iii)sub (iii) into (ii), 4y 1/3(10 y)=254y(3) (10 y)=25(3)12y 10 y=75y=5sub y=5 into (i)x-5=10x=15
2006-10-18 7:00 am
1) 設：較小的數為 m, 較大的數為 n
n - m = 10 ... (1) ----- 兩個數之差為10
4m + nx1/3 = 25 ... (2) ----- 較小的數4倍 = 4m, 較大的數的1/3 = nx1/3, 和 = 即是相加
從 (1), m = n - 10 ... (3)
代 (3) 入 (2), 4 ( n - 10 ) + nx1/3 = 25
4n - 40 + n/3 = 25
3 ( 4n - 40 + n/3 ) = 3 ( 25 ) ----- 全式左右乘大三倍
12n - 120 + n = 75
13n = 195
∴ n = 15
代 n = 15 入 (3), m = ( 15 ) - 10
∴ m = 5
∴ 較小的數是 5, 較大的數是 15 。
2) x ÷ 8 = 5 ... 3 ----- 此句可有可無, 若您是小學生就要列明
x = 8 x 5 + 3
x = 43
∴ 貼紙的總數是 43 張。
n - m = 10 ... (1) ----- 兩個數之差為10
4m + nx1/3 = 25 ... (2) ----- 較小的數4倍 = 4m, 較大的數的1/3 = nx1/3, 和 = 即是相加
從 (1), m = n - 10 ... (3)
代 (3) 入 (2), 4 ( n - 10 ) + nx1/3 = 25
4n - 40 + n/3 = 25
3 ( 4n - 40 + n/3 ) = 3 ( 25 ) ----- 全式左右乘大三倍
12n - 120 + n = 75
13n = 195
∴ n = 15
代 n = 15 入 (3), m = ( 15 ) - 10
∴ m = 5
∴ 較小的數是 5, 較大的數是 15 。
2) x ÷ 8 = 5 ... 3 ----- 此句可有可無, 若您是小學生就要列明
x = 8 x 5 + 3
x = 43
∴ 貼紙的總數是 43 張。
參考: 數 學 中 四 ． 五 ． 全 級 第 一 名
2006-10-18 6:26 am
1)設x,y是該數
x-y=10--------------------------i
4y+x/3=25--------------------ii
from---i,y=x-10
puty=x-10 into ii
4(x-10)+x/3=25
4x+x/3=65
x=15
putx=15 into i
y=5
2)有貼紙
8*5+3
=43張
x-y=10--------------------------i
4y+x/3=25--------------------ii
from---i,y=x-10
puty=x-10 into ii
4(x-10)+x/3=25
4x+x/3=65
x=15
putx=15 into i
y=5
2)有貼紙
8*5+3
=43張
2006-10-18 6:26 am
LET X AND X+10 BE THE LARGER & SMALLER NUMBERS RESPECTIVELY.
(X + 10) * 4 + X* (1/3) = 25
4X + 40 + (1/3) X = 25
4又 1/3 X = 25 - 40
13/3 X = -15
X = -15 / (13/3)
X = - 45/13
(X + 10) * 4 + X* (1/3) = 25
4X + 40 + (1/3) X = 25
4又 1/3 X = 25 - 40
13/3 X = -15
X = -15 / (13/3)
X = - 45/13
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